I like checking the flop in position. Hypothetically, if I were out of position on that flop, I would prefer a bet and then shut down to any call or raise. Checking OOP is more likely to win a bet off of TT, but that only helps if you're planning on calling. It also opens the door to being bet off the best hand. Also, I like being able to limit the bet size for those situations that I'm crushed, rather than leave it up to my opponent to decide. Against a very tight or passive player, I do like a check/fold approach better, because he's folding a worse hand if you bet and he won't bluff it if you check.
I'd say the turn is an easy fold, as I think you realized immediately after you called. It's really grasping at straws to think that he might be betting an underpair at this point, and every other hand beats QQ. Looking at the hand from the villain's perspective, the ten is a very bad card for him to bluff. Now QQ is literally the only hand he can get to fold. AQ and TT are now monsters. Also, it's a very very very bad idea to draw to the straight, because the odds
aren't nearly good enough to draw, and your outs might not even be live.
What if the turn were a blank? If he bets now, it depends the player you're up against. If he is hyper-aggressive, I think you can call.
Otherwise, I'd still lay it down. Betting out of position on a strong board shows a lot of strength, and I'd respect that versus all but the most loose aggressive opponents.