Based on the name and my understanding of the TF2 class, a Heavy is a front-lines tanky soldier guy. But that doesn't really seem to be his role in XCOM. Assault soldiers are better at being in the front lines with their mobility and defensive abilities.
What, then, is the heavy supposed to be doing on the battlefield? What are the general strategies that are useful for heavy soldiers?
Heavies are your primary damage dealers.
By the way: with the "Enemy Within" DLC, the assault class can theoretically out-damage the heavy. The "Close and Personal" skill grants them one free shot per round against an enemy within 4 tiles. This can be followed with "Rapid Fire" for a 2nd and 3rd shot in the same round. "Close Combat Specialist" can give them another free shot during the enemy turn when an enemy moves within 4 tiles for a total of 4 shots per round. But keep in mind that the assault can only use this potential when played in a very aggressive and risky way, while heavies can do their damage while camping behind a full cover.
The main purpose of heavies, early on, is a panic button: if you pull too many sectoids, thin men, and floaters all at once, you can nuke a fair number of them with the heavy's missile, with a near 100% chance to hit (the tooltip says 90%, but most of the 10% misses land very close to the target spot, and usually hit everything you were aiming at). It's also quite effective against mutons hiding behind cars, vans, or trucks, since the secondary vehicle explosion happens immediately.
They're also great when you have tough enemies hiding behind destructible cover, and want to improve others' aim by blowing it up.
Mid and late game, they're your primary means of taking out deadly robotic units via shredder rockets and/or heat ammo.
Often, when you build your first heavy, you'll be tempted to take the wrong skills, because some of the worthless ones sound pretty good...I know I took almost every wrong skill on my first one, so I think a big part of knowing what role a heavy should play is knowing how to build one:
Heavy Skills
At corporal, Bullet Swarm makes them very effective when you have a swarm of enemies advancing on you, and helps to make up for the fact that heavies have the worst aim of any XCOM soldiers. Holotargeting is usually not as useful: a hit from a heavy is worth more than a hit from any other class (except sniper), more shots generally results in more damage than a measly 10% aim bonus against one unit, and there are better options (Bullet Swarm, Shredder Rocket, the assault's Run and Gun + Rapid Fire, the sniper's Head Shot) when you need to quickly focus something down.
At sergeant, Shredder Rocket gives you a second panic button against large groups of weak enemies, and an excellent way to deal with deadly robotic units: hit it/them with a shredder, and the damage amplification will help the rest of your crew take it/them out quickly. Suppression is generally not as useful, in part because an alien that's dead is less likely to hit you than an alien with -30% aim, in part because it burns too much ammunition: it requires two of your heavy's three ammo to use the skill, meaning you lose the option of using Bullet Swarm on the following turn, and you can't keep an enemy suppressed for more than one turn. It often leaves you out of ammo in deep trouble. On the other hand, Shredder Rocket gives you an additional option when you're out of ammo. The aim penalty on the reaction shot (if it happens) is also pretty big for a heavy, whose aim isn't very good to start with.
Compare that to a support's Rifle Suppression, which a support can use two turns in a row even before Ammo Conservation, which doesn't prevent taking two shots in a turn (since a support can't anyway), and remember the support's aim is second only to the sniper, so the reaction shot penalty isn't as big a deal, which makes the support usually the better option for suppression, if you like to use it.
At Lieutienant, HEAT Ammo is the clear winner over Rapid Reaction, and the number one skill that makes heavies worthwhile: do you want two shots of reaction fire, given a heavy's low chance of connecting on a reaction shot? With the second shot fired only if the first one hits?? To boost the rate at which your heavy runs out of ammo??? Or do you want double damage against the deadliest enemies in the game, and the ability to take one out single-handed if both shots from bullet swarm hit?
At Captain, both choices are an option: grenades are another guaranteed hit area-effect weapon, which is useful given the heavy's poor aim, and, like rockets, they're useful for destroying cover and exploding vehicles that aliens are hiding behind for bonus damage. If you like your heavies to carry grenades as their accessory, it's the obvious choice.
On the other hand, two extra tiles' radius on your rockets from Danger Zone makes it easier to get large numbers of enemies in the blast radius, and is the only option if you prefer to use a scope to boost the heavy's poor aim, or anything other than a grenade.
The bonus radius on suppression would almost make for an argument to consider suppression, but in my experience, aliens rarely end their turn within two tiles of another alien, so suppression remains single-target most of the time. (If you could aim the diameter five area of suppression fire, instead of having to center it on a specific alien, that might be different, as you'd often be able to suppress three instead of just one if you could center the suppression fire on open space.)
At Colonel, a third rocket is generally more useful than +2 damage on the two rockets you already have.
A Heavy's primary role is damage output. Heavies have the earliest access to being able to fire twice in a round (Snipers need to be maxed rank to do that), making them extremely good early on. Their Rocket Launcher is also great early on because 6 damage is enough to kill just about anything until you run into Chrystalids and Mutons.
In my opinion, Heavies are wonderful in the early game, but underpowered later on. I found that their lack of aim (their base aim at maxed rank is 75, whereas Supports have 90) is workable in the early game because enemies don't have much to help them avoid shots. Your Heavies can reliably hit around 50-60% of the time, most of the time, which is decent. Later in the game, many enemies have special abilities that help them avoid hits. I found that, even if an enemy was wide open, my Heavies could usually only hit around 30-40% of the time, which is relatively unacceptable. Rocket Launchers are also a lot less exciting when they only take off 30% of an enemy's health. Their Heat Ammo is REALLY nice for taking out Sectopods, though. 30 damage crit ftw.
The best use for Heavies, if you can avoid getting too attached to your soldiers, is probably to take advantage of their being great early on to have them baby other soldiers until other soldiers are higher ranks, then sideline your Heavies for other classes. Personally, though, I get too attached to my soldiers, and can't side out my Heavies when they've been so good to me all game. :(
He is supposed to lay down covering fire on enemies to prevent their movement. Some promotions increase squad accuracy against pinned down enemies.
He is also supposed to use his rocket launcher to destroy cover and the enemies behind it. It's useful to put him up ahead with some extra hp and let him suppress and blow enemies to bits so your team can flank (or snipe!).
Think of them as a heavy weapons team in certain games or in real-life combat: Relatively low mobility, but high damage output, specialized/explosive/armor-piercing weaponry, and suppressive fire.
As you said, Assaults fill a "tankish" role as well as a scouting role. Heavies are the only class other than snipers that can shoot their primary weapon twice in a turn (with associated skill), which should indicate they can be more useful when used in a defensive capacity.
Heavy class, as others have said, is for suppression and "massive damage" (rockets). The idea of a 'tank' doesn't really hold, as that's more about ability to take damage or deal close quarter damage.
In play, I tend to put my heavies "mid field". That is, assaults up front, then heavy, with support bringing up the rear. Sniper covers any forward advance before moving up, depending on the map.
Hello just reading through all the above and realized that my play style is quite different from most people that have answered this question. Heavies are by far what I call as close as possible to the X-COM the original in the fight against the giant single eye @ Cydonia: You had an inventory grid and I would just cram the soldier with heavy plasma on 1 hand with extra clips, psi amp on the other hand, blaster launcher in back pack, 1st blaster ammo in the back pack, 2nd & 3rd bomb ammo in the belt, an electro flair, and the rest with as many alien grenades and proximity grenades, and the flying suit.
So to mimic the original X-COM I built my heavy with the following skills: shredder rocket and 1 more rocket giving it a total of 3 blaster bombs. I gave the heavy grenadier for 2 alien grenades, if only there were prox grenades. Bullet swarm to mimic auto shot, and rapid reaction - kinda like saving time units for snap shot and just sit in the corners waiting for aliens at the base.
I debated between psi suit vs. archangel suit vs. titan vs. ghost for psi ready soldiers and after some playing around, in the end I went for ghost suit. Ghost suit is just too good as you run as far as u can without triggering the enemy to move, and on the next turn I'd have so many opening moves to choose from: bullet swarm or mind control for single enemies when they are close by, grenade if their clustered but too close to friendlies, or blaster if i can hit a lot without hurting friendlies.
This was so good I decided to have 4 heavies like this. All 3 heavies go cloak, run in and surprise fireworks. Now the good thing about running into the enemies with ghosted heavies is that you can mind control them and before the control wears off group them up and grenade/blaster bomb em to death or even use their own grenades on em while clustered. So my heavies are the front of the line. I usually go with 4, followed by 2 medics for health patch up. In the end game, it was mandatory to have one of my heavy's go with psi suit as a volunteer, but now I know it's not needed to have the highest will power soldier to finish the game. Although that heavy was kinda fun with 3 blaster bombs and rift. I'd take ghost armor any time. 4 ghosting blaster heavies is a total of 12 blaster bombs per mission, so blasting fun (just remember by late game you have everything you want and you don't need to worry about the loot).
I tend to take the Heavies along to get at the Cyberdisks, Chrystalids and Sectopods, also the rockets are brilliant for weakening squads of Mutons for capture. I must admit I rarely uses anything but the Heavies with Support-backup due to the difficulty in reseraching pistols, sniper-rifles and the things the assault-class uses.
Given the heavy's low accuracy late game, i find that if i use it for direct attacks, i end up reloading saves and reordering my attacks so that my heavy actually hits. I find that bullet swarm is a great way to get a mulligan more than a chance to do damage, he rarely hits both times. Last couple play throughs, i have had two different heavies, one for early game and one for late game.
My early heavy takes holotargeting and suppression. The reason for this is, for a starting team with ballistic weapons my average %hit was around 50-60%. This is terrible. I use suppression because if i can't count on getting kills, i find i would rather count on the aliens NOT getting kills. I use holo to increase the odds of my teammates hitting the target and leveling up instead of the heavy. I find suppression is my main source of early interrogation volunteers(before ghost armor) as well. I whittle a group of enemies down to one, then have my support and heavy alternate reloading and suppressing to allow my "shock trooper" to close in for the stun.
After I have all the tech i need (ie dont need weapon fragments or other lootables from the mobs/UFOs) i spec out a new heavy (ensuring he is psi so that he can actually hit his targets when i need him to) for explosions, destruction and mayhem. My team doesn't have trouble hitting anymore at colonel and suppressing is a waste of time and bullets. But mostly late game, i find i only keep them around for the occasional oops pull where i need to take out a group of mutons so i can face off with the berserker that is drooling on my assault.
Lastly, If i know what types of enemies are going to be on the map, and the numbers are somewhat small, I drop the heavy for another assault, support, or a forward sniper. I prefer to have a team that can move across a map quickly dispatching single enemies nearly guaranteed.
The heavy is the damage dealing and crowd control class, with the capability of shredding any alien dumb enough to go within point blank range. I also use heavies equipped with chitin plating to draw the fire from the aliens, while assaults scout, flank and kill them at point blank range.
This is supported by the heavy skill will to survive, and is even easier with ammo conservation in the foundry.
Equip them with carapace or titan armor, and aliens will be more likely to target them.
