Do I miss value by 4bet-shove hidden Fullhouse on turn IP?

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Do I miss value by 4bet-shove hidden Fullhouse on turn IP?

Blinds: $0.25/$0.50 (6 Players) BN: $88.98
SB: $118.56
BB: $59.73 (Hero)
UTG: $20.39
MP: $24.17
CO: $45.30
Preflop ($0.75) Hero is BB with 9 6
4 folds, SB raises to $1.00, Hero calls $0.50
Flop ($2.00) 6 J 6
SB bets $0.75, Hero calls $0.75
Turn ($3.50) 6 J 6 9
SB bets $2.00, Hero raises to $8.00, SB raises to $15.50, Hero raises to $57.98 and is all in, SB folds
Final Pot BB wins $32.78
Rake is $1.72

I'm a hyper aggressive style player in 50NL.(31/21,3b 10) But I have only 25 hands playing history of my villain.(28/28/3b 17, CBF 100,CBT 100) And no specific note on him. I assume my stats look a bit aggressive to him as well.

I think all the plays before the turn are quite standard. Although 96o is a pretty bad hand, I have good odds to call with most of my hand. And I think I can outplay my opponent and take down pot often enough to make this preflop call +ev. Therefore I think floating this flop is a standard play.

I wanted to extract value by raising villain turn's barreling which he shows strength for his hand.(lots of good pair or strong draw), while my range still being weak and polarized(lots of hand I could float flop and have draw on turn), to either make him call with his worse pair or induce him bluff my raise.

And then he 3bet 2x my bet which I wasn't sure what my optimal play is, to 4bet shove or flat to let him barrel? which is a more +ev play?

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