AAJ9sss 3 bet pot as SB vs BTN flop 662 no fd for hero.

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AAJ9sss 3 bet pot as SB vs BTN flop 662 no fd for hero.

Blinds: $0.10/$0.25 (6 Players) SB: $32.82 (Hero)
BB: $25.00
UTG: $4.56
MP: $64.98
CO: $20.08
BN: $58.49
BTN 24/18/14 (VPIP/PFR/3bet preflop stats)
Preflop ($0.35) Hero is SB with A 9 A J
3 folds, BN raises to $0.85, Hero raises to $2.80, BB folds, BN calls $1.95
Flop ($5.85) 6 2 6
Hero checks, BN checks
Turn ($5.85) 6 2 6 8
Hero bets $5.60

On the flop I was thinking that given the preflop action I had a range advantage as I have all the AAxx and value heavy hands in my range whereas BTN would have 4 bet me if he these, but that BTN had the polarity advantage as I have many fewer 6s in my range than he does.

I decided to check call the flop as I did not want to face a raise from a FD etc as my range is so heavy in AA, other overpairs and high cards. I also figured I would not be getting many better hands to fold and some weaker hands were more likely to bet than call a Cbet.

I took the check behind as a sign of weakness as I think being IP he might bet a FD plus over pair or BD straight draw etc and so I bet. I hoped to get some value from weaker hands, pair plus FD or straight draw etc.

I reviewed the hand in Vision and it says cx flop 48% and bet 1/3 pot 52%. After the check behind it says cx 44% and bet 1/2 pot 56%. So my bet size was bad.

Any thoughts on my thought process? Also how does being 130BB affect our play?

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