NL50z - We flop a set OOP

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NL50z - We flop a set OOP

Blinds: $0.25/$0.50 (6 Players) BN: $108.34
SB: $89.80 (Hero)
BB: $69.09
UTG: $78.40
MP: $50.57
CO: $22.62
Preflop ($0.75) Hero is SB with 4 4
3 folds, BN raises to $1.50, Hero raises to $5.50, BB folds, BN calls $4.00
I 3bet as i dont want to have a flatting range here in SB Vs Btn
Flop ($11.50) 6 4 7
Hero bets $3.60, BN calls $3.60
I am betting small OOP in a lot of 3bet pots. Here, we dont mind overcards peeling as we basically have the nuts
Turn ($18.70) 6 4 7 T
Hero bets $12.43, BN calls $12.43
Heating up on the turn we bet bigger to deny equity and will still be way ahead of range
River ($43.56) 6 4 7 T 5
Hero bets $30.50, BN raises to $86.81 and is all in, Hero calls $37.77 and is all in
Final Pot BN wins and shows a straight, Four to Eight.
SB lost and shows three of a kind, Fours.
BN wins $178.10
Rake is $2.00

Villain is playing a lot of hands but sample it small

Akward spot on river where SPR means i think i cant shove here profitably. Maybe i should have bet bigger on flop and turn to only have a small overbet left here to shove? Or should we avoid altering betsizes because of SPR. I feel that a check is too weak as we miss value from a lot of hands like 99, JJ, 76, AT, 75. which check back. I think most sets would raise turn so his range here i think is not too strong. Once he shoves instantly though we are likely beat but still just seems bad to fold....?

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