Check/Fold TPTK in a 3bet Pot? (NL 100)

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Check/Fold TPTK in a 3bet Pot? (NL 100)

BN: 172.13
SB: 101
BB: 169.27 (Hero)
UTG: 209
HJ: 109.25
CO: 31.60
Preflop (1.50) (6 Players)
Hero was dealt A K
UTG folds, HJ folds, BN folds, BN raises to 2, SB folds, Hero raises to 7, BN calls 6
Flop (16.50) 5 K J (2 Players)
Hero bets 11.55, BN calls 11.55
Turn (39.60) 2 (2 Players)
Hero bets 27.72, BN calls 27.72
River (95.04) 9 (2 Players)

Villain is unknown

I think the Flop and Turn a pretty std. I bet a bit bigger, becasue of our stacks and the FD on the Turn which I guess is fine...

My thoughts about the River:

1. of all Villain is not calling much worse but has a lot of better hands in his range

Even if he is calling some QQ or AJs combos it is still a flip (he is also capable of holding 55). Given that a bet is pretty BE to slightly -EV with a ton of variance.

2. If we check and Villain bet he is rarely bluffing becasue I do not see him Jx betting and I do not give him a lot of busted draws on this board. 

So what are your thoughts?

How do you play the river?

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