In Act 3, Scene 1, Macbeth directly expresses his fears of Banquo in a long soliloquy.
To be thus is nothing;But to be safely thus.--Our fears in BanquoStick deep; and in his royalty of natureReigns that which would be fear'd: 'tis much he dares;And, to that dauntless temper of his mind,He hath a wisdom that doth guide his valourTo act in safety. There is none but heWhose being I do fear: and, under him,My Genius is rebuked; as, it is said,Mark Antony's was by Caesar. He chid the sistersWhen first they put the name of king upon me,And bade them speak to him: then prophet-likeThey hail'd him father to a line of kings:Upon my head they placed a fruitless crown,And put a barren sceptre in my gripe,Thence to be wrench'd with an unlineal hand,No son of mine succeeding. If 't be so,For Banquo's issue have I filed my mind;For them the gracious Duncan have I murder'd;Put rancours in the vessel of my peaceOnly for them; and mine eternal jewelGiven to the common enemy of man,To make them kings, the seed of Banquo kings!Rather than so, come fate into the list.And champion me to the utterance!
Three times Macbeth says he fears Banquo: once when he says, "Our fears in Banquo stick deep," and then when he says, ". . . and in his royalty of nature / Reigns that which would be fear'd," and next when he says, "There is none but he / Whose being I do fear." What he fears the most, judging from this soliloquy and other statements he makes, is that Banquo will take the witches' prophecy at face value, as he himself has done, and will decide that the best way to insure that his heirs will be kings of Scotland is to assassinate Macbeth.
Macbeth knows that Banquo is nearly positive that he gained the throne by murdering Duncan. Although Banquo would never consider murdering the legitimate king, as Macbeth has done, he would probably have no compunctions about murdering a usurper who murdered the legitimate king himself. As far as Macbeth knows, Banquo may be planning that murder as he speaks his soliloquy.
He is afraid of Banquo not only because Banquo sees right through him, and not only because Banquo obviously has a strong motive to murder him, but because he senses that Banquo has a superior intellect and therefore can outsmart him and end up beating him at his own game of murder and usurpation.
Macbeth feels that he committed the regicide only for the benefit of Banquo's descendants. He suspects he was doing exactly what Banquo expected and that Banquo will reap the real benefits from the assassination of Duncan. But he can't really know what is going on in Banquo's mind because Banquo has a superior intellect. He is treating Macbeth with the utmost courtesy and respect, but this is hardly reassuring; rather it is somewhat unnerving.
What is really going on in that man's subtle mind? Maybe Banquo intends to kill him. Maybe Banquo intends to organize a plot against him. Maybe he is just waiting for fate to bring about the fulfillment of the witches' prophecy that he would be father to a whole line of kings. "He hath a wisdom that doth guide his valour / To act in safety."
The viewer does not know what Banquo is thinking, either. It seems most likely that he is just biding his time, waiting to see what will happen next. But his calmness, patience, and formal deference have an unnerving effect on the more emotional Macbeth, and as he delivers his soliloquy he has already made the rash decision to have Banquo and his son Fleance ambushed and murdered.