100 Euro 6 max. Possibly overplayed FD on the turn?

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100 Euro 6 max. Possibly overplayed FD on the turn?

Blinds: t75/t150 (6 Players) BN: 19,745
SB: 16,626
BB: 21,116 (Hero)
UTG: 30,223
MP: 17,912
CO: 14,921
No reads on villain, playing 24/20 over 82 hands.
Preflop (225) Hero is BB with 6 7
3 folds, BN raises to 300, SB folds, Hero calls 150
Flop (765) 8 K 3
Hero checks, BN bets 300, Hero calls 300
Turn (1,365) 8 K 3 9
Hero checks, BN bets 1,037, Hero raises to 4,050, BN calls 3,013
River (9,465) 8 K 3 9 2
Hero bets 8,775, BN folds
Final Pot BB wins 9,465

In game, I thought this would be a decent FD combo to raise since I do not block any of his broadway bluffs that are barreling turn plus I have zero showdown unimproved. Looking back, I am not sure the portion of his range he is folding is worth taking this huge variance heavy line, not to mention we could get shoved on and have to fold our draw. Is there any upside to raising the turn with such a strong draw?

Assuming he gets to the river with 91 combos (KK+, 99-88, 33, AdKd, AhKh, AcKc, AsQs, KdQd, KhQh, KcQc, AsJs, QsJs, AsTs, QsTs, JsTs, As9s, Kh9h, Kc9c, Qs9s, Ts9s, Kd8d, Kh8h, Kc8c, As5s, As4s, 5s4s, As3s, As2s, AKo, K9o-K8o),
and assuming he folds everything except AA, KK, 99, 88, 33, K9s, K9o, K8s, K8o (36 combos), we have 36/91 = he calls 39,56 % of the time.

Our bet only needs to work 48% of the time to be profitable.

As played in the turn, would you rather choose a smaller river bet and target exclusively his missed FDs?

Thanks.

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