Instead of pushing right there, I would 3-bet to 25-30. That way he'll have a harder time folding AQ, AJ, but effectively he has to pay you off eventually either by raising all in, or by calling on the turn when he's getting 4:1 on a call.
One reason to push right there if I have one of my most common player notes on the guy which simply says "hero" - meaning that he likes to raise c-bets and call down bluffs, in which case a shove might look weaker to him.