I would definitely raise the turn here, and if he three-bets it then call down to the river. I think my opinion is a bit skewed because I saw the river action, but on the turn I really think you're up against a weaker queen here rather than two pair that just filled up. He has a huge range of hands here, I think. He could be three-betting the flop with a number of draws, perhaps a pair of nines and a flush draw, or top pair and a straight draw. Maybe he's getting aggressive because the pot is heads up. He might even have aces, who knows?

Anyway, I think the flop is fine.

The river action is kind of weird on his part. Why the hell he went for the check-raise is beyond me, so I have no idea what he had.