Why did Nazgûl spare the other hobbits at Weathertop?

Question

In the fight at Weathertop, the Nazgûl injured Frodo and left. They waited for him to pass to the shadow and become a wraith, but they did not kill the other hobbits on Weathertop: Sam, Merry, and Pippin. Moreover, Merry had an enchanted sword which he later used to harm the Witch-king during the Battle of the Pelennor Fields. Apparently, the Nazgûl did not recognize such a powerful sword.

This negligence allowed Pippin and Merry to get the Ents to march against Isengard and reduce the pressure on Rohan. By not killing Samwise Gamgee, the Nazgûl made it possible for Sam to carry Frodo to Mount Doom. As a result, the outcome of the War of the Ring is affected directly.

While book answers are preferred, movie answers are also welcomed.

Answer 1

The Nazgûl were there to take the Ring. Frodo had the Ring. So they targeted Frodo. Before they could slay (or wraithify, at any rate) Frodo and take the Ring, Aragorn drove them off — but not before they poisoned Frodo. After that, they were not terribly worried, since:

They tried to pierce your heart with a Morgul-knife which remains in the wound. If they had succeeded, you would have become like they are, only weaker and under their command. You would have become a wraith under the dominion of the Dark Lord; and he would have tormented you for trying to keep his Ring, if any greater torment were possible than being robbed of it and seeing it on his hand.

(The Fellowship of the Ring)

Aragorn also points out they didn't expect to be resisted:

There seem only to have been five of the enemy. Why they were not all here, I don't know; but I don't think they expected to be resisted. They have drawn off for the time being. But not far, I fear. They will come again another night, if we cannot escape. They are only waiting, because they think that their purpose is almost accomplished, and that the Ring cannot fly much further. I fear, Sam, that they believe your master has a deadly wound that will subdue him to their will. We shall see!

(The Fellowship of the Ring)

Additionally, Aragorn's resistance was substantial: the Ringwraiths are fearsome, but their chief weapon is fear. If you aren't afraid of them, and you wield fire, they aren't as deadly.

Sauron can put fire to his evil uses, as he can all things, but these Riders do not love it, and fear those who wield it. Fire is our friend in the wilderness. (The Fellowship of the Ring)

Their peril is almost entirely due to the unreasoning fear which they inspire (like ghosts). They have no great physical power against the fearless. (Letters)

They weren't there to go to war and slay everyone who stood in their way. Particularly at this time, they were moving in secret.

"I have an urgent errand," he said. "My news is evil." Then he looked about him, as if the hedges might have ears. "Nazgûl," he whispered. "The Nine are abroad again. They have crossed the River secretly and are moving westward. They have taken the guise of riders in black." (The Fellowship of the Ring)

They could not see the future and did not know that Merry and Pippin would play key roles in the war of the Ring. They were there to get the Ring and bring it to Sauron. And in fact, they were afraid of the Hobbits (at least of Frodo), in part precisely because of their swords.

[The Witch-king] had been shaken by the fire of Gandalf [from earlier], and began to perceive that the mission on which Sauron had sent him was one of great peril to himself both by the way, and on his return to his Master (if unsuccessful); and he had been doing ill, so far achieving nothing save rousing the power of the Wise and directing them to the Ring. But above all the timid and terrified Bearer had resisted him, had dared to strike at him with an enchanted sword made by his enemies long ago for his destruction. Narrowly it had missed him. How he had come by it — save in the Barrows of Cardolan. Then he was in some way mightier than the B[arrow]-wight; and he called on Elbereth, a name of terror to the Nazgûl. He was then in league with the High Elves of the Havens.

Escaping a wound that would have been as deadly to him as the Mordor-knife to Frodo (as was proved at the end), he withdrew and hid for a while, out of doubt and fear both of Aragorn and especially of Frodo. But fear of Sauron, and the forces of Sauron's will was the stronger.

("The Hunt for the Ring", Unfinished Tales)

Answer 2

Though Tolkien doesn't say this, he never insults the reader's intelligence. I believe it could also be surmised that Sauron didn't want them actually holding the Ring. He didn't want anyone having possession of the Ring, which was of great power, who might then oppose him and become, with its corruption and the time to learn its secrets, another Dark Lord or Dark Queen. A Nazgûl with the One Ring in his actual hands is something Sauron absolutely wouldn't have wanted except as the last need. They were his slaves, but Sauron had certainly known betrayal before as would any being and ruler in his supreme position. But my answer only makes sense with all that's written here. The Nazgûl didn't expect to lose, and another power was always at work, as stated here, for good that was unseen. Sauron was wise (as a fool because of his malice. He after all couldn't understand that anyone would want to destroy the Ring), but he feared greatly when the uncertainty of events took hold against him. I believe a Nazgûl actually holding the Ring was an uncertainty he was not willing to take.