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Tricky turn that hits villans range what to do?

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Tricky turn that hits villans range what to do?

Blinds: $0.10/$0.25 (6 Players) SB: $29.87 (Hero)
BB: $29.68
UTG: $28.22
MP: $25.80
CO: $25.00
BN: $25.00
Preflop ($0.35) Hero is SB with A A
2 folds, BN raises to $0.62, Hero raises to $2.20, BB folds, BN calls $1.58
Flop ($4.65) 3 9 Q
Hero bets $3.31, BN calls $3.31
Turn ($11.27) 3 9 Q J
Hero checks, BN bets $5.58, Hero calls $5.58
River ($22.43) 3 9 Q J 4
Hero checks, BN bets $13.91 and is all in, Hero folds
Final Pot BN wins $21.31
Rake is $1.12

Really could not come to a conclusion on this one do you continue to bet turn and then be committed to villains shove and do you call the river on a good card like the 4d?

I ran it in Equilab for the turn to the below result.

Board Qd 3s 9c Jh

Equity Win Tie
BU 41.44% 41.18% 0.26% 99+, 33, A9s+, K8s+, Q8s+, J7s+, T8s+, A9o+, K9o+, Q9o+, J9o+, T9o
SB 58.56% 58.29% 0.26% AdAc

Any feedback would be most appreciated this is my first hand post so hope it makes senseand really loving this site :)

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