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[NL5] TP value shove river?

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[NL5] TP value shove river?

Blinds: $0.02/$0.05 (6 Players) BN: $6.41
SB: $9.67 (Hero)
BB: $11.05
UTG: $6.51
MP: $5.97
CO: $7.23
Preflop ($0.07) Hero is SB with Q K
3 folds, BN raises to $0.13, Hero raises to $0.55, BB folds, BN calls $0.42
Flop ($1.15) 7 7 4
Hero bets $0.35, BN calls $0.35
Feels like a board we still have the advantage as the PFR and I decided to go for a range c-bet on this flop.
Turn ($1.85) 7 7 4 3
Hero bets $1.05, BN calls $1.05
Not a great card for us but neither for villain. We can still fold out many Ax hand which called the flop hence the bet. In hindsight I think we should a) bet bigger if we bet and b) pick a different hand like JTs as it blocks TT and JJ. Our king-high might be good here on occasion and we would love to see a free card. Is this reasoning sound?
River ($3.95) 7 7 4 3 K
Hero bets $7.72 and is all in
His range should consist of straights (65s is possible), many flushes, some monsters like a full house which decided to play it passively and a chunk of second best pairs like 88-JJ. Somthing lke KhTh might also be in his range. I think he would raise 7x most of the time. Given the good amount of strong hands in his range and uncertainty about him calling us with 88-JJ I like the check-back on this river. What do you think? Thanks!

Villain has $4.46 left on the river.

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