[curtains]

You should have raised more preflop, when you reraise with a hand like QQ you almost always want to give your opponent the chance to fold. You didn't do so here as they arent folding for 75 more. However I usually want action with this hand if Im ahead, so Id probably raise to 300 and put rest of the chips in on the flop. Allin is quite reasonable preflop as well.
On flop I'd bet something. I like to think that my opponents aren't generally creative enough to check raise bluff me. But they may be creative enough to bet the turn if I check the flop, and then I have no idea where I'm at. It's much harder for them to show false aggression if you show aggression yourself.
So umm, if I somehow got into your situation postflop, I'd bet something. btw I tend to look ahead in tournaments and anticipate such flop situations. I wouldnt want to be in a situation where I have 600 chips and there is 350 in the pot, because certain scary boards can still make my decision difficult. I'd like to manipulate the pot so that I'm making a decent size raise preflop, but also my postflop decisions will be automatic.