Cold 4bet bvb - do we valuebet river?

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Cold 4bet bvb - do we valuebet river?

BN: $100.50
SB: $195.52 (Hero)
BB: $196.08
UTG: $437.98
HJ: $122.30
CO: $122.67
BTN is a reg playing 23/18. RFI on BTN: 44%, Fv3bet: 60% 600 hands
BB is a reg playing 21/17. 4bet: 3.7, Cbet flop: 60% W$WSF: 47, 2k hands
Preflop ($1.50) (6 Players)
Hero was dealt Q Q
UTG folds, HJ folds, CO folds, BN raises to $2, Hero raises to $7, BB raises to $21.49, BN folds, Hero calls $14.49
Flop ($46.48) T 5 4 (2 Players)
Hero checks, BB bets $22.48, Hero calls $22.48
Turn ($91.44) 8 (2 Players)
Hero checks, BB checks
River ($91.44) 3 (2 Players)
Hero checks, BB checks
Final Pot
Hero has Q Q Hero wins $87.14

I put BB a linear range pre, something like AKo-AJo, KQo, KQ-KJs, AKs-ATs, AA-TT. 

Do you prefer a small 5bet, a shove or a flat pre? Why?

As played can we valubet otr? For me it seems like BB is capped at A-high, K-high and JJ and at the time I thought that he wont call me with worse often enough. 


Thanks

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