I couldn't find anyone mentioning anything to do with this at all.
I am assuming it is definitely not how I'm reading it, however:
Why does it sound like the fighter brute stacks damage on every hit?
Just reading it sounds like every time you hit the weapon damage increases by an extra 1d* whatever the level.
This can't be a thing but has anyone else read it like that?
When the Brute Force feature from "Unearthed Arcana: Three Subclasses" says:
Whenever you hit with a weapon that you’re proficient with and deal damage, the weapon’s damage increases by an amount based on your level in this class.
...it means that the weapon damage is boosted for that attack. The weapon itself isn't boosted, but the damage for that attack. The extra damage die gets added to the damage dice portion of damage as described in the basic rules:
Each weapon, spell, and harmful monster ability specifies the damage it deals. You roll the damage die or dice, add any modifiers, and apply the damage to your target. Magic weapons, special abilities, and other factors can grant a bonus to damage.
For example if you are a level 3 Fighter (Brute) attacking with a greatsword, the weapon damage for that attack would be 2d6+1d4 instead of 2d6. You would then add an ability modifier or other modifiers as normal for weapon attacks.
