[chuddo]

i would never fold this preflop.

often i would check-call the flop, and check-raise the turn all in, as you did. stacks/pot sizes are perfect for this line to have the +30% folding equity against an overpair to make this a profitable play.

one line i might consider is just calling his turn bet, and adding a couple of 'bluffing' outs in addition to my actual big draw.

such as any 9 that puts the 4 straight out there.
an A if KK/QQ is possible and he can put you on the A-flush draw.
a 10 that pairs the top pair.

if one of those cards fall i would be very tempted to lead right into him pretty big. he could still credit you with a flopped set, a turned straight, or that you just rivered him.

as far as what to bet on the end if you call his turn bet and then hit it is dependant on which draw comes in.

the best card would obviously be the offsuit 3 and i would either bet the pot, and contemplate a check-raise all in if would not check his AA/KK behind.

if the flush comes in i would be resigned to bet 3/4th the pot. likewise for the 9 for the 4-straight.