I think the biggest mistake here is just calling preflop, I like 3 betting or folding much better than calling, but as played is this an easy fold? There was some history with this player however, he double barreled AKs in a 3 bet pot when the board was 357J and I had QQ and called turn and river went check check.

Full Tilt No-Limit Hold'em, $0.50 BB (6 handed) Full-Tilt Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

SB ($45.85)
Hero ($54)
UTG ($78.30)
MP ($52.30)
CO ($53.05)
Button ($73.30)

Preflop: Hero is BB with J, K.
1 fold, MP raises to $1.75, 3 folds, Hero calls $1.25.

Flop: ($3.75) 9, 7, J (2 players)
Hero checks, MP bets $3, Hero calls $3.

Turn: ($9.75) 4 (2 players)
Hero checks, MP bets $7, Hero calls $7.

River: ($23.75) 2 (2 players)
Hero checks, MP bets $15, Hero ?

I think the bigger mistake was actually the call on the flop. I would've raised the flop, both to charge the draws and for more information. If he raised or called and then continued betting strong when the 3rd club came you could've more comfortably let the hand go, and it probably would've have cost you less money. Here you can't really tell if his bet on the flop was a standard continuation bet, a semi bluff with something like AcKc, or even an overpair.

Here you check called the flop with str8 and flush draws, and then called the turn after the 3rd flush card came. What could he imagine you have and still be betting? You mentioned that he double barreled the AK before, but that was on a seemingly innocuous board of low cards. He could've reasonably assumed that the board didn't help you much, and have been firing the second shot out to continue to represent an over pair. When you called on the turn he let the hand go and checked it down, which shows he's observant enough to realize he's up against a made hand that isn't going away. I'd fold.

Fold preflop

As played: lead turn, fold turn (or call down)

I like 3b preflop but I dont mind a call or a fold.

flop is hard because IF you c/r and he pushes, you need like ~38 but against reasonable pushing range I would say you have ~34. So c/r + calling might be slightly -ev and c/r + folding sucks with TPGK on a drawy board. I guess I would c/c and see what the turn brings. if I c/r I would call btw.

I probably just give it up on turn.