1/2, 10 player

utg: $300
co (Hero = T J) = $300

preflop:
utg/mp/hero limps, button raises to $7, blinds folds, utg/mp/hero calls

button seems like a good competent player. no idea what his small raise means.
normal raises at this table when there's limpers = $12+.

flop ($31): 3 7: T
utg bets $10, mp calls, hero raises to $40, button folds, utg calls, mp folds

utg loves playing any 2 suited cards. I've seen him win with Q4s from utg+1.
I take his small bet as a blocking bet to get a cheap turn card.

turn ($121): K
utg checks, Hero bets $80

it is possible he as KXs.
but I thought it was small compared to the huge risk of letting him get a free card since I put him on a flush draw.

What would you do?

Button is juicing the pot preflop, usually a small/medium pocket pair but possibly suited connectors also. Build the pot and hope he hits.

I think your line is OK but checking this turn is also good. You don't have a big hand and it is possible villain can have something like QhTh and already have you beat or have a flush draw that hit the king. This depends a bit on knowing just how weak villain can be calling the flop raise. If he can show up with low flush draws or the OESD then betting is good. If his EP limping range is mostly high cards then the turn helps him more often.

Preflop limp/call is meh, I'd rather open so that I can fire favorable turns like this one.

Turn is pretty terrible, spr is getting low and V def has KY, KXhh in range.

Not a fan of pre because of spots like this.

Neither option on the turn is great but I default to b/f here. Dudes a fish with super wide range of hands that we are still ahead most of the time.

I like the turn bet. Wet board, giving a free card seems like a mistake. Prob checking behind on most rivers, so get value here with a bet/fold line since Kxhh is def in his range.

I would have fold pre based on the number of limpers.

If I had to play JT, I would have raised pre instead of limping.

AP, I like the $80 bet.
I doubt he has KXs. Why would he bet into X amount of players with a KX type hand.

He might have 98, some heart combo, maybe a weak 7 or T.

I'd bet turn, and probably check river if check too.

Meh... I'm fairly non sophisticated, but I'd check. Not really looking to play a large pot with second pair poop kicker. Unfortunately this will most likely induce a bluff on the river and you'll really have no clue where you're at. I guess as played, you have to bet turn or accept the need to call safish rivers.