Hey guys so I recently played a MTT on pokerstars and I just want your guys opinion if I played this hand correctly or not. Blinds are at 250/500 with a 40ante, villain covers me and both of us are the deepest stacked players at the table. Looking back on this I feel like my 3bet sizing maybe was too big preflop since we were both deep? Would you guys check/jam on this dry of a flop or check/raise? Sick thing is I put villain exactly on JJ, TT, AK pre (and once he led out 1/2pot on flop I was sure he had JJ or TT) since I feel like he would probably 4bet me if he had AA, KK since both of us were deep and he was out of position (i think he was like UTG+1 or middle postion 1). Also his 3x raise pre also indicated to me that he probably didn't really want action on this hand, I felt like he might have maybe made his raise pre smaller if he had AA or KK to get some more action...

Here it is:

PokerStars Hand #111426204695: Tournament #858628251, $3.00+$0.30 USD Hold'em No Limit - Level XIV (250/500) - 2014/02/07 7:43:04 ET
Table '858628251 45' 9-max Seat #3 is the button
Seat 1: bmc.rocha (14611 in chips) 
Seat 2: HERO (16909 in chips) 
Seat 3: big_joker423 (5552 in chips) 
Seat 4: bozgoro (8657 in chips) 
Seat 5: mlody111111 (8745 in chips) 
Seat 6: B&O 139 (9046 in chips) 
Seat 7: haagsewillem (5475 in chips) 
Seat 8: DanLemes (18443 in chips) 
Seat 9: never.sleep8 (15487 in chips) 
bozgoro: posts small blind 250
mlody111111: posts big blind 500
*** HOLE CARDS ***
Dealt to HERO [Qd Qs]
B&O 139: folds 
haagsewillem: folds  
DanLemes: raises 1000 to 1500
never.sleep8: folds 
bmc.rocha: folds 
HERO: raises 2500 to 4000
big_joker423: folds 
bozgoro: folds 
mlody111111: folds 
DanLemes: calls 2500
*** FLOP *** [2d 6h 2s]
DanLemes: bets 3220
HERO: raises 9629 to 12849 and is all-in
DanLemes: calls 9629
*** TURN *** [2d 6h 2s] [Th]
*** RIVER *** [2d 6h 2s Th] [7h]
*** SHOW DOWN ***
DanLemes: shows [Td Tc] (a full house, Tens full of Deuces)
HERO: shows [Qd Qs] (two pair, Queens and Deuces)
DanLemes collected 34988 from pot
HERO finished the tournament in 1453rd place
*** SUMMARY ***
Total pot 34988 | Rake 0 
Board [2d 6h 2s Th 7h]