What does Macbeth think as he anticipates the murder of Banquo?
this is in Act 3
The answer to this is in Act 3, sc. 1 approximately ll. 52-76. Here Macbeth says he is afraid that Banquo suspects he had something to do with Duncan's murder beause of Banquo's "royalty of nature" and because Banquo has "...a wisdom that doth guide his valor...". Macbeth goes on to say that he fears Banquo. Then Macbeth laments the Weird Sisters' prophecy that Banquo's descendants would become kings while they had no such prophecy for Macbeth, ""They hailed him father to a line of kings. / Upon my head they placed a fruitless crown...". Macbeth talks on about this for most of the rest of this soliloquy. It frustrates Macbeth endlessly that he is not to have children who might follow his royal footsteps. In scene 2 of Act 3, Macbeth tells his wife that they haven't rid themselves of their problems by killing Duncan, they have only traded one problem for another problem ("We have scotched the snake, not killed it"). Right now, the uppermost problem in Macbeth's mind is getting rid of Banquo and Fleance.
When Macbeth orders the assassins to kill Banquo and his son Fleance, it is an indication that he has truly gone over to the side of evil. Even when he murders King Duncan, he feel extreme remorse and wishes he could undo it. However, with more and more violent deeds, he shows that he has actually become the tyrant he feared he'd be. Even though his plot worked and he has now become the King of Scotland, he is still not content. He still feels extremely uneasy. He thinks that if the prophecy were true thus far (because he has become both the Thane of Cawdor and the King of Scotland, both prophetic visions that seems impossible at first), then the rest of the prophecy that hasn't come true yet must eventually come true. He becomes obsessed with the witches' proclamation that Banquo's children would become kings, and that Macbeth would never have a line of descendants. Although Macbeth will become royalty, Banquo will father royalty. Macbeth thinks that if this is true, then he will have killed Duncan for nothing. He will have sullied and darkened his soul not for his own sake, but for the sake of Banquo's sons, whom he does not care about.
Another point is that it is extremely important to have children to carry on your lineage. If you have descendants, you "live forever" in a way. If you don't, your legacy dies with you. It cannot go on. Macbeth and Lady Macbeth have been trying to beget an heir for many years, but they have been infertile and unsuccessful. It angers Macbeth that someone else's children will become king after him.
Macbeth feels eager for the death of Banquo and Fleance. He has become coldblooded enough to order the murders of his good friend and his friend's young son. Every time he sees or thinks about Banquo, he feels sick and uneasy. He tells the hired murderers that they must kill Banquo in order to make everything better.