• that he had to suffer so much turmoil and unsettle his peace for them whilst his legacy would die with him. He is so overwhelmed by this thought that he utters a furious outburst in which he expresses his disgust.

In the end, Macbeth decides that to prevent what the witches' had predicted, Banquo has to be killed. Banquo is too great a threat:

Rather than so, come fate into the list.And champion me to the utterance!

He alone should benefit from the witches' predictions. He later affirms the fact that Banquo must die after he had spoken to the assassins whom he had hired to kill Banquo and his son, Fleance. Fleance has to be killed to negate the witches' prediction regarding Banquo's heirs.

It is concluded. Banquo, thy soul's flight,If it find heaven, must find it out to-night.

Macbeth is so determined to have Banquo killed that he has plotted to have the pernicious deed performed that same night.

Macbeth's suspicions arise not only from what he has observed and what he knows about Banquo, but also from how Banquo had responded to his suggestion, when they speak in Act ll, scene l: 

MACBETH

If you shall cleave to my consent, when 'tis,It shall make honour for you.

BANQUO

So I lose noneIn seeking to augment it, but still keepMy bosom franchised and allegiance clear,I shall be counsell'd.

Macbeth is clearly suggesting that Banquo should support him and that he would reward him when the time comes. Banquo's cryptic reply suggests that he would lose none of the honor he already has if he chooses to enhance it as long as he retains his loyalty to his king (Duncan). It is obvious that Banquo would never betray his liege.

Macbeth's fear of Banquo is that, through him, the second part of the witches' initial prophecy will come true. According to the weird sisters, Macbeth would rule Scotland, but it would be Banquo's heirs--not Macbeth's--who would eventually inherit the throne. After Macbeth does become king, the idea that he has murdered Duncan for the benefit of Banquo's sons and grandsons is repugnant to him. Macbeth rails about the "barren scepter" the witches have placed in his hands, and he refuses to accept that he has given to Hell his very soul, his "eternal jewel," so that Banquo's line will enjoy power. 

Furthermore, Macbeth has some real concerns about Banquo in Macbeth's "here and now." Macbeth knows that Banquo is a man of good character and conscience whose loyalty lies with Scotland, not with Macbeth. If Banquo were to know Macbeth's role in Duncan's death, he would seek justice. This possibility troubles Macbeth:

Our fears in Banquo stick deep,

And in his royalty of nature reigns that

Which would be feared. 'Tis much he dares;

Macbeth then acknowledges that Banquo is a genuine threat to him: "There is none but he / Whose being I do fear." It is Macbeth's fear and jealousy that prompt him to have his former good friend murdered.

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 fear

Thou 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)

In Act 3, Scene 1, Macbeth directly expresses his fears of Banquo in a long soliloquy.

To be thus is nothing;But to be safely thus.--Our fears in BanquoStick deep; and in his royalty of natureReigns that which would be fear'd: 'tis much he dares;And, to that dauntless temper of his mind,He hath a wisdom that doth guide his valourTo act in safety. There is none but heWhose being I do fear: and, under him,My Genius is rebuked; as, it is said,Mark Antony's was by Caesar. He chid the sistersWhen first they put the name of king upon me,And bade them speak to him: then prophet-likeThey hail'd him father to a line of kings:Upon my head they placed a fruitless crown,And put a barren sceptre in my gripe,Thence to be wrench'd with an unlineal hand,No son of mine succeeding. If 't be so,For Banquo's issue have I filed my mind;For them the gracious Duncan have I murder'd;Put rancours in the vessel of my peaceOnly for them; and mine eternal jewelGiven to the common enemy of man,To make them kings, the seed of Banquo kings!Rather than so, come fate into the list.And champion me to the utterance!

Three times Macbeth says he fears Banquo: once when he says, "Our fears in Banquo stick deep," and then when he says, ". . . and in his royalty of nature / Reigns that which would be fear'd," and next when he says, "There is none but he / Whose being I do fear." What he fears the most, judging from this soliloquy and other statements he makes, is that Banquo will take the witches' prophecy at face value, as he himself has done, and will decide that the best way to insure that his heirs will be kings of Scotland is to assassinate Macbeth.

Macbeth knows that Banquo is nearly positive that he gained the throne by murdering Duncan. Although Banquo would never consider murdering the legitimate king, as Macbeth has done, he would probably have no compunctions about murdering a usurper who murdered the legitimate king himself. As far as Macbeth knows, Banquo may be planning that murder as he speaks his soliloquy.

He is afraid of Banquo not only because Banquo sees right through him, and not only because Banquo obviously has a strong motive to murder him, but because he senses that Banquo has a superior intellect and therefore can outsmart him and end up beating him at his own game of murder and usurpation.

Macbeth feels that he committed the regicide only for the benefit of Banquo's descendants. He suspects he was doing exactly what Banquo expected and that Banquo will reap the real benefits from the assassination of Duncan. But he can't really know what is going on in Banquo's mind because Banquo has a superior intellect. He is treating Macbeth with the utmost courtesy and respect, but this is hardly reassuring; rather it is somewhat unnerving.

What is really going on in that man's subtle mind? Maybe Banquo intends to kill him. Maybe Banquo intends to organize a plot against him. Maybe he is just waiting for fate to bring about the fulfillment of the witches' prophecy that he would be father to a whole line of kings. "He hath a wisdom that doth guide his valour / To act in safety."

The viewer does not know what Banquo is thinking, either. It seems most likely that he is just biding his time, waiting to see what will happen next. But his calmness, patience, and formal deference have an unnerving effect on the more emotional Macbeth, and as he delivers his soliloquy he has already made the rash decision to have Banquo and his son Fleance ambushed and murdered.

Macbeth’s fear of Banquo stems from the witches’ prophecies in Act I, Scene 3.  Of course, Macbeth is originally enraptured by the witches’ startling predictions that he will become Thane of Cawdor and King. However, when Banquo inquires about his destiny, the witches’ three-line response slowly destabilizes Macbeth and leads him to murder his former confidant and best friend.

The first witch tells Banquo that he will be “lesser than Macbeth but greater” (1.7.66). The second witch tells him that he will be “Not so happy, yet much happier” (1.7. 67). Finally, the third witch tells him that “Thou shalt get kings, but thou shall be none” (1.7.68). This final line means that while Banquo himself will not be king, his sons will rule. Consequently, Macbeth agonizes over the fact that he killed Duncan and consigned himself to hell only to see Banquo’s children take control of the throne. He worries that Banquo and his son Fleance will pose a grave threat to his power and life. In fact, the threat of Banquo’s children continues to haunt Macbeth even after Banquo’s death; in Act IV, Scene I, the witches show Macbeth a line of kings followed by Banquo’s ghost. This is a clear sign to Macbeth that Banquo’s children will form a dynasty.

In fact, one could even argue that Macbeth is not afraid of Banquo; Macbeth is terrified of Banquo’s children.

The only two people to hear the prediction of the witches were Macbeth and Banquo. Banquo, knowing these predictions, can readily suspect Macbeth of the murder of Duncan. In order to take care that this does not happen, Macbeth needs to have Banquo killed. His reason for having Fleance killed is that the witches told Banquo that he would be the father of kings, though none himself. Therefore to prevent Fleance being king, Macbeth must have him killed also.

I believe there are 2 reasons for this. One is due to the second part of the witches' predictions. Banquo was told he would not be a king, but his children would become king. This helps to secure the thrown for Macbeth. Also, Banquo is aware of the predictions the witches gave Macbeth and he saw his reactions. He would be the first logical character to become suspicious of Macbeth.

An interesting question. Macbeth had to kill Banquo (or tried to do so, and Fleance too) because of the other half of the prediction: Banquo's sons would be kings. That means Macbeth's line would be displaced, so Macbeth is trying to secure his heritage.