NL16 AJ 2nd barrel vs. fish

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NL16 AJ 2nd barrel vs. fish

Blinds: $0.08/$0.16 (6 Players) BN: $42.89
SB: $33.58 (Hero)
BB: $25.87
UTG: $16.00
MP: $19.61
CO: $15.36
39/22, 60 hands, afq:60
ft3bets: 0/0 (ip/oop)
ftcbets: 14/50/-
Preflop ($0.24) Hero is SB with J A
3 folds, BN raises to $0.48, Hero raises to $1.60, BB folds, BN calls $1.12
Value 3bet. Do you EVER not 3betting here your valuerange since its gonna be hard to fight for pots with him if we missed?
Flop ($3.36) T K 4
Hero bets $1.60, BN calls $1.60
Not sure if i shouldnt just give up. His ftcbet stats are telling me that i dont have EV+ cbet but i was thinking in these categories:

a) its 3bet pot so i can use small cbet sizing for bluff,
b) board is not wet
c) i hit some EQ with my gutter and Ahigh, J on the turn could be good for me either.

Turn ($6.56) T K 4 K
Hero bets $3.36, BN calls $3.36
I think turn bet is more justified than flopcbet.
K on turn means that he have less valuehands in his range than on flop. I need only 33%FEQ with my sizing and i think i may had it. And ofc i still have outs on river.
River ($13.28) T K 4 K 2
Hero checks, BN bets $6.40, Hero folds
Final Pot BN wins $12.68
Rake is $0.60

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