Flop 3bet sizing 100bb deep

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Flop 3bet sizing 100bb deep

SB: $45.92
BB: $54.03
HJ: $16.08 (Hero)
CO: $46.85
BN: $16
Villain is a 23/15 9.3% 3bet and 20% fold to 3bet over 1.2k hands.
Preflop ($0.24) (5 Players)
Hero was dealt A A
Hero raises to $0.48, CO calls $0.48, BN folds, SB folds, BB folds
Flop ($1.20) 2 T 9 (2 Players)
Hero bets $0.88, CO raises to $2.88, Hero raises to $7.04, CO calls $4.16
I think 3betting is right here the villain has 53% fold to cbet 39% raise cbet IP and 26% OOP so I'm ahead of their range and they're definetly capable of raising with draws and there are a lot of ugly cards that could come so I'd like to get more money in now.

What I'm not sure about is the sizing I think I have too much to jam so I'm not sure how big I should bet. I tried to go for a sizing that I thought was the biggest I could make it while not pot committing myself but I don't know if that's right or not.
Turn ($16.16) 2 T 9 9 (2 Players)
Hero bets $8.52, and is all in, CO folds
Final Pot
Hero wins $14.78

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