(Gerundial noun phrase). Literally, a series of movements executed in the sport of boxing in which one participant dodges and parries his opponent's punches by moving quickly back and forth, and up and down, so as not to present a stable target. Used figuratively to describe behavior that is less than straightforward, esp. in dealings with others.
Niggaz be bobbing and weaving and shit, I ain't feelin' that, y'all need to come correct.