BTN vs BB combo draw. Turn/river play and bet sizing question

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BTN vs BB combo draw. Turn/river play and bet sizing question

Blinds: $0.50/$1.00 (6 Players) CO: $90.90
BN: $114.02 (Hero)
SB: $47.50
BB: $80.00
UTG: $22.15
MP: $25.00
CO is fish. BB is good, TAG reg. 550 hands. VPIP/PFR is 23/16 overall with 9% 3-bet from BB.
Preflop ($1.50) Hero is BN with Q T
2 folds, CO calls $1.00, Hero raises to $4.50, SB folds, BB calls $3.50, CO calls $3.50
Flop ($14.00) A 9 8
BB checks, CO checks, Hero bets $4.62, BB calls $4.62, CO folds
Turn ($23.24) A 9 8 6
BB checks, Hero checks
I should barrel turn after picking up equity, right? However, while I was deciding what bet size to use, I timed out.

What's a good bet size here? Overbet? Maybe something standard like 75% pot? I'm not sure I have much of a range/nut advantage here. Turn card hits both our ranges pretty well.
River ($23.24) A 9 8 6 J
BB checks, Hero bets $29.00
BB checks again. Since his range is very capped, I decide to go for overbet. Is it a good spot to use this bet sizing?

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