In the beginning of Act 2 of Shakespeare's Macbeth, how do Banquo and Macbeth regard each other?
At the beginning of Act Two of Shakespeare's Macbeth, Macbeth and Banquo have become very different people than who they were at the play's start.
It is after the banquet to honor Duncan at Inverness (Macbeth's home), and Banquo and Macbeth meet by chance. Banquo mentions that he has dreamt of the witches, and comments that some of what the witches have said has come true for Macbeth. (This will be a concern to Macbeth because Banquo was the only one with him to hear the predictions, especially the one about Macbeth being king...this would make the honorable Banquo suspicious if Duncan were to die at Macbeth's castle.)
Macbeth lies and says he doesn't think about the predictions. However, he asks Banquo if they could discuss the situation again in the near future. Banquo agrees to do so, whenever it is convenient to Macbeth. (This is clearly just casual discussion.)
With some foreshadowing for the audience, Macbeth approaches Banquo to see how far he can trust his friend. Macbeth says that if Banquo will have his back (support him) when the time is right, Macbeth will make it worth his while (reward him).
Banquo, unlike Macbeth, cannot be swayed from his honor and duty to king and his own sense of moral character. He responds:
So I lose none/ In seeking to augment it, but still keep / My bosom franchised and allegiance clear, / I shall be counselled.
In other words, Banquo is telling Macbeth that as long as he does not need to compromise his sense of right and wrong, and as long as he can serve his king loyally, he will consider what Macbeth might ask of him. Basically, Banquo has told Macbeth that he will remain true to the things he holds dear and honorable.
This is, of course, important for Macbeth to know; if Duncan dies on Macbeth's watch, it will be Banquo who will challenge his friend's part in the murder, most especially because of the witches' predictions. This also shows the audience how distanced the two men have become, when they were once both honorable servants to Duncan.
So although they seem friendly enough, Macbeth is keeping his ideas of the witches' predictions tucked away, and asking to see how far he can trust Banquo. Banquo is full of praise for how graciously the Macbeths have entertained the king, but he is also no fool: he can imagine, I'm sure, that Macbeth is asking where his allegiance lies, especially with Macbeth's promise of a reward under the right circumstances. Banquo lets Macbeth know, in no uncertain terms, that he is honor-bound to support his king and will follow the dictates of his heart to do what is ethically correct. Each man knows where the other stands.