DJ riders don't have to muscle the bike around as much as BMX or trials though, they just go fast and the ramp does (most of) the work. Saying that, I ride shows with a DJ rider and his bike is just under 11kg, he really hates the wind though.
BMXs are generally not that heavy either, ~10kg seems to be fairly average for a street setup. I'd be after a less effort for hops and spins than any potential stability a heavier bike might add.