[50NLz] Is 3 barreling on this runout a correct play with higher then 25% frequency?

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[50NLz] Is 3 barreling on this runout a correct play with higher then 25% frequency?

PokerStars - $0.50 NL FAST (6 max) - Holdem - 6 players

BTN: 97.9 BB
Hero (SB): 103.5 BB
BB: 100 BB
UTG: 110.76 BB
MP: 88.94 BB
CO: 100 BB VPIP 24 PFR 22 Fold to 3 Bet 44 (220 hands)

Hero posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has Qc Kh
fold, fold, CO raises to 2.5 BB, fold, Hero raises to 10 BB, fold, CO calls 7.5 BB

3 bet with KQo from the SB against the CO looks ok to me

Flop : (21 BB, 2 players) 3c Ts Ac
Hero bets 9 BB, CO calls 9 BB

Having a gut shot and blocking flush draws I decide to bet out and represent the A as I have more Ax hands then villain in my range.

Turn : (39 BB, 2 players) 7c
Hero bets 28 BB, CO calls 28 BB

Get more equity (second NUT flush draw) so I decide to make another bet (sizing could be smaller see river).

River : (95 BB, 2 players) Th
Hero bets 56.5 BB and is all-in, CO calls 53 BB and is all-in

This is the part where I am very unsure about if that is ok. Afterwards I don't think this 3 barrel is working often enough given the stack sizes. So I either should bet smaller on the turn such that I can bet larger on the river or just give up.

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