Similar hands have been discussed, but I'd still like to see some opinions on this turn.

Villain is representing a set or an unlikely straight, but he might have picked up a draw on this turn, or he might be overplaying TT-JJ. His stats after 200+ hands are 28/15/1 -- he has only 3bet once in 83 occasions preflop, so he probably likes calling preflop with most of his strong-but-not-monster hands rather than 3bet. Although that might be too weak of an inference from 200 hands.

The question is: do we shove this turn and chalk it up as a cooler when we run into a set, or do we fold and risk being exploited?

He might overplaying TT,JJ or some draws like 57cc,86cc but there are many value hands in his range like sets, 34 two pair and straights A5s,65s. I ll mostly fold on this spot and i call only if i m sure he is whale or have a note that villain overestimates hands. Although i know its hard sometimes to find fold in these spots.

You would expect a villian that overplays overpairs to raise on the flop.

They can have all sets and straights here 56s A5s. Given the size of the raise it pretty much pot commits the villain, you can fold here. I would expect draws to be raising smaller on the turn and you block some combos with the Kc if they have floated flop with two overs AKs KQs etc.

Fold to turn raise yes

so this hand is very different to your previous hand and heres why, its 4 way to the flop and youve bet on a board youre unlikely to have any bluffs on given how multiway it is and youve raised UTG the only reasonable bluffs would be A5 + A3 with a backdoor FD and that seems quite ambitious lets say you do have these well thats 6 combos of bluffs vs value 89s 9Ts A9s 99 TT JJ QQ KK AA = 42 combos (not sure if you raise 44 UTG so didnt want to add that), so ypur range is pretty narrow on the flop which in turn will narrow his range... his pre flop range should be very pocket pair heavy i dont think after 200 hands you can assume he doesnt 3bet JJ QQ pre, given his pre flop range and your narrow flop and turn betting range i think hes given you a let off on the turn i would fold..