In the beginning of the play, Macbeth and Banquo seem to be good friends. However, by Act 3 they are just keeping up appearances. Each is suspicious of the other.
Banquo is suspicious of Macbeth.
Banquo used to respect Macbeth, but he is a clever man. He was there when the witches told both of them that Macbeth would be king. He worries that Macbeth wanted to be king so badly that he did something terrible and killed Duncan when he didn’t get what he wanted.
Thou hast it now: King, Cawdor, Glamis, all,
As the weird women promised, and I fear
Thou play'dst most foully for't: (Act 3, Scene 1, enotes etext p. 40)
Banquo goes on to comment that everybody is speaking highly of Macbeth and “their speeches shine” (p. 40), but they are in for a surprise because what they think is not really true.
Banquo begins to wonder if Macbeth is out to get him. After all, he was told by the witches that his sons would be kings. This makes him a threat.
Let your Highness
Command upon me, to the which my duties
Are with a most indissoluble tie
Forever knit.(20) (Act 3, Scene 1, enotes etext p. 40)
Banquo goes out of his way to demonstrate that he is a friend still, and a faithful subject.
Macbeth is worried about Banquo.
Banquo has every right to wonder about Macbeth, because while he is acting like a friend he is plotting to kill Banquo.
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 fear'd. (Act 2, Scene 1, p. 42)
Macbeth is basically saying that it is all fine and good to be king, but you have to be safe. Banquo, since his sons will be king, is a threat. Macbeth no longer cares about their friendship. He arranges to have Banquo and his son murdered. He is actually only asking what Banquo will be doing not to be friendly, but to know where to send the murderers.