Bet again...

With your smooth call pre-flop... I don't think he puts you on AA or KK. Your bet on a flop indicates a Q in your hand. If he was behind, i.e. trying to catch an A or K... there is no way he can call at this point.

If he was slow playing AA or KK waiting to trap you for all your chips on the turn, he is going to be very scared you caught up by tripping your queens.

with so much money in the pot.... I think you have to fire a second barrel.

He'll fold way to many hands at this point to make betting a negative EV play.