Macbeth does not attempt to kill Banquo himself because he no longer has to do his own dirty work. He has become king and can delegate such deeds to others. Being king makes Macbeth conspicuous. It would be harder for him to murder Banquo than it was to murder Duncan; but it is much easier to establish an alibi for killing Banquo or anybody else, because he can have the killing done for him while he makes an appearance in front of numerous other people. As king he could probably have ordered Banquo executed (and he might have even framed him for the murder of Duncan to justify the execution), but he probably didn't feel sufficiently secure in his new position as absolute ruler. No doubt he would like to be thought of as a benevolent monarch, but he quickly learns that this is impossible because too many people, including Banquo and Macduff, feel sure he gained the throne by the worst kind of treachery.
As far as Macbeth's motivation for killing Banquo is concerned, this seems to be thoroughly covered in his soliloquy in Act 3, Scene 1, quoted below in full.
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. ’Tis much he dares,
And, to that dauntless temper of his mind,
He hath a wisdom that doth guide his valor
To act in safety. There is none but he
Whose being I do fear; and under him
My genius is rebuked, as it is said
Mark Antony's was by Caesar. He chid the sisters,
When first they put the name of King upon me,
And bade them speak to him; then prophet-like
They hail'd him father to a line of kings:
Upon my head they placed a fruitless crown(65)
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 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 seed of Banquo kings!
Rather than so, come, Fate, into the list,(75)
And champion me to the utterance!
Macbeth is afraid of Banquo. He realizes that Banquo should have a strong motivation to assassinate him in order to make it possible for his own descendants to become the kings of Scotland, as promised by the three witches. Macbeth also feels sure that Banquo sees right through him and knows intuitively and deductively that Macbeth killed Duncan in order to become king. Macbeth thinks he can cheat fate by killing Banquo and thereby preventing him from producing heirs to the Scottish throne. No doubt Macbeth is already planning to have Fleance murdered along with his father.