Checking behind on the flop with AA

[Sponger15SB]

$200nl 6max, I've got $111 cause I don't have the roll to buy in full. Opponent is 75vpip/11pfr after 70 hands.

Villian limps UTG, folded to me, I raise to $8 with AA, folded to Villian who calls.

Flop is Q 7 3r
Villian checks extremely quickly and I decide to check behind.

Does anyone do this? My opponent probably has nothing, and he was reasonably agressive. Should I check to hope he bets into me with nothing or is this incredibly stupid and I should just STFU and bet the flop already.