As his paranoia increases, Macbeth becomes very anxious about Banquo, as the witches told him his sons will become kings.
In the beginning of Act III, at Forres, the castle that was King Duncan's and is now Macbeth's, Banquo, who is a guest, realizes Macbeth has all that "the weird women" promised him. Also, he fears Macbeth had a hand in his own fortune: "Thou play'dst most foully for 't" (Act III, Scene 1, line 3). Then, because of the turn of events, Banquo wonders if the witches' prophecy about himself will come true.
Later, Banquo informs Macbeth that he and his son Fleance plan to ride for an hour; Macbeth extends good wishes for an enjoyable ride and urges Banquo to return for the banquet that evening.
After Banquo and his son's departure, Macbeth expresses his fear of Banquo, who heard the prophesy about him and received prophesies of his own.
To be thus is nothing, but to be safely thus—
Our fears in Banquo stick deep.
And in his royalty of nature reigns that
Which would be feared. . .
He hath a wisdom that doth guide his valor
To act in safety (Act III, Scene 1, lines 50-56).
When Macbeth says he fears Banquo's "being," he means he is worried that since the predictions of the witches have come true for him—even though he helped cause some of this reality—those predictions about Banquo's becoming the father of kings may also become real. Since Macbeth has no heirs, he fears he may have sold his soul to the Devil in order to make Banquo's sons kings as the witches have foretold.
Only for them, and mine eternal jewel [his soul]
Given to the common enemy of man [the Devil to whom he has sold his soul],
To make them kings, the seeds of Banquo kings! (Act III, Scene 1, lines 71-73)
In addition, he worries Banquo may take some actions himself for his "safety." Macbeth hires two murderers and sends them to kill Banquo and his son.