Banquo fears Macbeth because he knows that Macbeth has heard the witches' prediction that Banquo's sons will be kings. Since the witches' prediction that Macbeth would become Thane of Cawdor has become true, Banquo is anxious that Macbeth will try to kill him because the third witch also said, "All hail, Macbeth, that shalt be King hereafter!" (1.3.61).
Then, in Act III after Macbeth has been made king after Duncan has been murdered at Macbeth's castle, Banquo's soliloquy opens Act III:
Thou hast it now: king, Cawdor, Glamis, all,As the weird women promised, and I fearThou played’st most foully for ’t. (3.1.1-3)....If there come truth from them—As upon thee, Macbeth, their speeches shine—Why, by the verities on thee made good,May they not be my oracles as well,And set me up in hope? But hush, no more. (3.1.6-10)