So this is early/mid stage of tournie.  It's a Pokerstars Deep Stack tourney so 5k was starting stack, hence the super deep stacks.

Opponent is 23/9/8 has called from BB 4/7 times. 40% River Agg but only 5 hand sample for river.

Poker Stars No Limit Hold'em Tournament – t150/t300 Blinds + t25 – 9 players – View hand 2510439
TournamentPokerEdge.com Hand History Converter

MP2: BB = 49.0, t14714
CO: BB = 178.2, t53461
Hero (BTN): BB = 178.4, t53516
SB: BB = 93.5, t28042
BB: BB = 102.7, t30813
UTG: BB = 60.0, t17992
UTG+1: BB = 51.3, t15387
UTG+2: BB = 48.5, t14563
MP1: BB = 113.8, t34155

Pre Flop: (t675) Hero is BTN with Q A
3 folds, MP1 raises to t600, 2 folds, Hero raises to t1699, 1 fold, BB calls t1399, MP1 calls t1099

— I 3b AQ w the intention of 3b/f just because at these stakes it's never worse.  I also have position and should be able to take it down w a lot of CBs.  Don't have him on much of a range but I'd discount the best hands.  

Flop: (t5472) 4 3 Q (3 players)
BB checks, MP1 checks, Hero bets t2099, BB calls t2099, MP1 folds

So i'm gonna fire this flop either way and take it down quite often after 3b pre.  He calls the CB, now I think he can have all pairs but over pairs 33-JJ, QJ, KQ, AQ, 34,A3, A4, 45, 56, 67? along w flush draws.  

Turn: (t9670) 5 (2 players)
BB checks, Hero checks

This hits a part of his range and I don't know if my check was right.  It feels like this is one of the worse cards for me but deathly terrible. Should I be going for 3 streets? 

River: (t9670) J (2 players)
BB bets t6890, Hero ??

Now this seems like probably one of the worse cards in the deck.  His whole flop calling range has gotten there on the turn and river.  Can I ever call here?