Banquo has good reason to be suspicious of Macbeth--to think Macbeth killed Duncan and to be afraid that his own life and his son Fleance's life are in danger. Even before Duncan's body is discovered by Macduff, Banquo was acting extremely cautiously for a man who was a guest in another man's castle. In Act 2, Scene 1, Banquo is carrying his sword. As the scene opens he gives it to Fleance, but then where he sees someone coming he says
Give me my sword--Who's there?
It is Macbeth, who is planning to murder King Duncan. But Macbeth knows he should also murder the King's two sons, Malcolm and Donalbain, because they stand in the way to his succession to the throne. This is a big undertaking for one man. He cautiously sounds Banquo out about joining him in a conspiracy, since they have the same interests. Banquo cannot have his heirs become kings until Duncan and his sons are disposed of, and according to the witches' prophecies Macbeth will have to become king before Banquo's prospects can be realized. Here is the pertinent dialogue in Act 2, Scene 1:
I dreamt last night of the three Weird Sisters.
To you they have showed some truth.
I think not of them.
Yet, when we can entreat an hour to serve,
We would spend it in some words upon that business,
If you would grant the time.
At your kindest leisure.
If you should cleave to my consent, when 'tis,
It shall make honor for you.
So I lose none
In seeking to augment it, but still keep
My bosom franchised and allegiance clear,
I shall be counseled.
Good repose the while.
Thanks, sir. The like to you.
Banquo knows that Macbeth has as good as asked him to join him in an assassination plot. He turns Macbeth down. Banquo knows that Macbeth wants to become king immediately. As king, Macbeth would be an even greater threat to Banquo and Fleance than he is now. Macbeth would have much greater power to injure Banquo and his son, even to have them executed on some trumped-up charge. Banquo does not want to be a traitor and an assassin, and he knows that his best strategy is to wait. If the prophecies of the Weird Sisters are accurate, then he will have to be dead before his heirs become kings. He would like to live many more years, and it might actually be many more years before their prophecies concerning him are realized. As it turns out, Macbeth becomes king, then Malcolm becomes king in his place, Banquo is dead, and still the prophecies regarding Banquo's sons and grandsons have yet to be fulfilled.
What Banquo suspects is that Macbeth killed Duncan and that Macbeth is capable of doing anything. If Macbeth can kill the king, he certainly wouldn't have qualms about killing Banquo and Fleance. And Banquo knows that Macbeth must have a motive to do so, because Macbeth would not want to kill Duncan for Banquo's benefit. Macbeth himself speaks of this in a soliloquy in Act 3, Scene 1.
For Banquo's issue have I filed my mind;
For them the gracious Duncan have I murdered,
Put rancors in the vessel of my peace
Only for them, and mine eternal jewel
Given to the common enemy of man
To make them kings, the seeds of Banquo kings.
Rather than so, come fate into the list,
And champion me to th' utterance.
Macbeth frequently talks about opposing Fate itself. This is the only thing that makes him seem heroic. Here where he says "champion me," he is challenging Fate to come and fight him in a formal combat. It might be said that the main conflict in the play is between Macbeth and Fate, with Macbeth the protagonist and Fate the antagonist. In the end Fate proves invincible. Fate intends for Macbeth to die, just as it intends for all of us to die. It is always invincible. Fate can be visualized as a black knight astride a black horse with his face hidden by a black helmet.