This is a difficult question because, in this complex plot, Shakespeare incorporates at least four forces that all conspire to contribute to Macbeth's downfall. These forces are King Duncan's choices and his men's reactions at the opening of the play; the Weird Sister witches and their predictions; Lady Macbeth's ambition and villainy; Macbeth's weak inner character.
One might simply say that Macbeth made his own decisions and therefore ultimately bears the final responsibility for his downfall. But isn't that missing one of Shakespeare's principle points, though, by overriding it and throwing it out of the cauldron of contemplation? Isn't it the same point that Alan Paton makes in Cry, the Beloved Country? This point being that external forces have power to sway and turn good to bad through influence alone.
Let's examine these forces to sort out an answer. Duncan rewards Macbeth by making him Thane of Cowdor, "And with his former title [of Cowder] greet Macbeth." for which all Duncan's followers were glad as they hold Macbeth in great esteem. Yet Duncan awards succession to the crown to his son, Malcolm, not to Macbeth. A feeling of disappointment pervades the gathering, leading Macbeth to his first traitorous thoughts, though directed toward Malcolm:
[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. Stars, hide your fires;
Let not light see my black and deep desires:
Next, Macbeth encounters the witches who interfere with riddles and paradoxes suggesting Macbeth will be King, irrespective of the line of succession. Macbeth encounters the power-crazed Lady Macbeth, whose lust for power is so great because she herself seeks to have it. Both these forces have enormous influence because they are bound up with fierce and dramatic emotion: exposure to fierce emotion is the surest way to implant a mental construct.
Then Macbeth encounters his own inner weakness. Weakness seems a contradiction to his success as a victor in battles. Yet maybe this is part of Shakespeare's point: inner character is complex and multifaceted, not one-dimensional, so extreme influences may always find an entry point.
So, how much responsibility does Macbeth bear? From a perspective of the role of Fate, it may be said he bears little responsibility because Fate set him about with corrupting influences. From a perspective of moral culpability, it may be said he bears full responsibility, but the weight of it is strongly mitigated (lessened) by the extreme influences bearing in upon him.
An even more interesting question might be how much responsibility falls on Duncan, the witches, and Lady Macbeth respectively:
yet do I fear thy nature;
It is too full o' the milk of human kindness
Banquo heard the witches, too, but was free of Duncan's failed expectations and of Lady Macbeth's venom. It seems the end analysis must be that, while Macbeth bears full responsibility for his actions, the blame is heavily mitigated, or lessened, and shared by these strong, overpowering forces that influenced him.