How did the witches contribute to Macbeth's downfall in William Shakespeare's Macbeth?
It is clear the witches in William Shakespeare's Macbeth do have some power; however, it is also clear that Macbeth hears what he wants to hear and acts of his own free will (well, except for his wife's pressuring him).
The witches make some predictions to Macbeth and Banquo, and of course the two soldiers are amazed at what they hear. When Banquo hears that he will be "lesser than Macbeth, and greater," "not so happy, yet much happier," and "thou shalt get kings, though thou be none," he is surprised and puzzled. When Macbeth hears his the witches hail him as Thane of Glamis, Thane of Cowdor, and "Macbeth, thou shalt be king hereafter," he is surprised but enthralled. When Macbeth is suddenly pronounced Thane of Glamis (by King Duncan), he believes. From that point on, Macbeth acts as if he is going to be king.
He is relatively humble at first, saying:
Macbeth is moved by his ambition, however, and he changes his behavior and thinking based on that. In the very next scene, Macbeth has already changed his mind and intentions when he learns Duncan has named his son, Malcolm, as his heir, next in line to the throne:
[Aside] The Prince of Cumberland! that is a step
On which I must fall down, or else o'erleap,
For in my way it lies.
The witches did nothing to make him change; Macbeth's ambition has already begun to work on him. The witches do not force him to listen to his wife's goading, nor do they compel him to commit any of the murders he will commit.
On the other hand, the witches do have some power. We know that one of them was irked at a sailor's wife for not sharing her chestnuts and took some revenge on the woman's husband at sea:
I will drain him dry as hay:
Sleep shall neither night nor day
Hang upon his pent-house lid;
He shall live a man forbid:
Weary se'nnights nine times nine
Shall he dwindle, peak and pine:
Though his bark cannot be lost,
Yet it shall be tempest-tost.
Look what I have.
It is clear that she can do some things, such as keep the man up with foul weather. She also reveals the truth that she does not have the power to kill him: "Though his bark cannot be lost." WHile they clearly have some powers (because some of their predictions come true and they do impact others' lives), they have no power to turn Macbeth into a murderer. That is something he does himself.
One of the central questions of the play is whether the witches knew what Macbeth would do and just appeared to predict it or whether they were deliberately trying to goad Macbeth into acting on his secret ambitions by promising him he would be king. The witches are a factor in Macbeth's choices, but in the end he makes his own decisions.