Opponent turn calling range

Not sure why you would 3bet pre-flop with a hand that can play well post-flop and you don't have a good sample on his fold to 3bet stats. As played I would most likely give up the turn. I doubt he will fold to often on a blck turn card like this and he can have a lot of Ax hands in his range he would call the flop with.

Cheers,
SDK1987

very tricky spot.
i don't think most villains are folding any decent Ax (if any Ax at all) to a second barrel buvco - i am relatively conservative and i certainly won't.
however, can they fold a midpair/gutshots/backdoor floats? probably. and sometimes, a miracle happens and you bink the river, or they have JT and you win at showdown.

what is actually the frequency of each hand type in villain's range? we'd have to look more carefully.

Pre it's a mixed strategy so no problem. Can call, can 3bet.
I'd cbet smaller OTF, and then have more FE OTT (as villain's range would be wider) where I'd bet bigger. Notice though that usually a "profitable turn barrel with low equity" is pretty much a nonsense (unless you happen to be in such an autoprofit spot that you can bet any two but it should be rare).