AKo in a 4bet pot - how do I plan this hand on the flop

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AKo in a 4bet pot - how do I plan this hand on the flop

Blinds: $0.15/$0.30 (6 Players) CO: $30.16
BN: $42.36
SB: $30.60 (Hero)
BB: $95.28
UTG: $35.96
MP: $17.36
22/20 3bet 9.5% fold to 3bet 49%. I have seen him shove jacks in a BTN vs CO raising battle.
His value betting range does not include thin bets on later streets but he will try to take pots early in hands. I honestly don't know how much range thinking he does
He has seen me play for deception once.
Preflop ($0.45) Hero is SB with K A
2 folds, CO calls $0.30, BN folds, Hero raises to $1.50, BB raises to $3.30, CO folds, Hero raises to $6.30, BB calls $3.00
Flop ($12.90) 3 Q 8
Hero checks, BB bets $4.05, Hero calls $4.05
Turn ($21.00) 3 Q 8 J
Hero checks, BB checks
River ($21.00) 3 Q 8 J 6
Hero checks

Preflop, I noted the unforced error of a small 4bet size already. I'll still take advice on how to size it :)

On the flop, I am a 2:3 underdog against the range I gave him and nothing I beat calls a bet right? The only reason to bet is for my range, correct?

After the turn, not much I lose to folds to a shove and not much I beat calls, so I should just escape the hand.

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