PokerStars No-Limit Hold'em Tourney, Big Blind is t50 (8 handed) internettexasholdem.com

MP2 (t1510)
Hero (t5745)
Button (t2675)
SB (t875)
BB (t2005)
UTG (t1660)
UTG+1 (t1690)
MP1 (t1240)

Preflop: Hero is CO with Q, A.
2 folds, MP1 calls t50, 1 fold, Hero raises to t200, Button calls t200, 2 folds, MP1 calls t150.

Flop: (t675) 5, 3, 2 (3 players)
MP1 checks, Hero bets t500, Button folds, MP1 calls t500.

Turn: (t1675) J (2 players)
MP1 checks, Hero ???

He has 540 left.

Reasons for checking: free card vs overpair is so juicy, and I don't want to just throw in more money when I have no pair and seemingly little FE.

Reasons for betting: if he has me beat, getting it in with 6-10 outs is not that awful with the pot size. I could also easily have the best hand (this is a 5/45, remember), and if so, getting called or not is fine, but checking through is kinda gross.

Also, should I have played differently earlier in the hand to avoid this? Is the CB on the flop good in general?