What is our optimal line in 3bet pot w/ AQ boardway + flushdraw?

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What is our optimal line in 3bet pot w/ AQ boardway + flushdraw?

Blinds: $0.25/$0.50 (6 Players) BN: $57.69
SB: $97.07 (Hero)
BB: $53.16
UTG: $177.18
MP: $26.73
CO: $50.00
Preflop ($0.75) Hero is SB with A Q
UTG raises to $1.25, 2 folds, BN calls $1.25, Hero raises to $6.50, BB folds, UTG calls $5.25, BN calls $5.25
Flop ($20.00) 7 J K
Hero checks, UTG bets $12.25, BN folds, Hero raises to $79.50, UTG folds
Final Pot SB wins $42.50
Rake is $2.00

So the original raiser was playing 1 table, and in 13 hands his stats were 46/31/25, also he had 50% fold to 3bet in two opportunities. He also c-bet the one opportunity he had. The in button flatter is playing 24/21/8 over 500 hands folding to 3bets 23/30.

My inicial thoughts is that if I continuation bet this hand into 3 people I am just going to get into a really awkward spot where I get flatted and there is a weird stack to pot ratio on the turn. I also thought this likely weaker player UTG was just going to do weird stuff. Maybe I need to just bet flop and shove turns if I get called with my advantage on this board. As far as what I'm going to do with value that is an interesting spot if I have AK w/ no club, or if I have a number of other hands. Any suggestions or ideas would be appriciated. Is this a spew to just x/shove all in on flop though? I thought without the nut flush draw at some frequency we are jut putting in $90 into a pot of $32 drawing dead, totally dead. I didn't enjoy this spot....lol.

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