Chekov's motivation...? Why, the Klingons killed his brother! Plus, he's been consistently racist about that ridgeheaded scum. So along comes Admiral Cartwright and tells Chekov he's to be a kingpin in a great plan to kick the Klingons when they are down, and the only thing he needs to do is betray his captain and fellow officers - the same people who shook hands with the repulsive enemy just one movie ago. (Plus, he's still bitter about that Vixis thing.)
And, you know, he's never quite been the same since Khan put that thing in his brain, and V'Ger zapped him with that plasma bolt, and he fell off that aircraft carrier and cracked his skull . . .