He had fold to 3b of 56%. Villain had folded 1/2 times in 3b pots but only 29% in non 3b pots with a high raise cbet %. Had seen him float oop on J 2 2 with 9 7 in non 3b pot. He had very high flop, turn agro frequency.

Is all that enough to assume villain can have 5 6s, 6 8s and some random floats in his range and its a fine bluffcatch on turn? Or should this be a flop check-call?

Is the turn usually a check-fold without villain being too loose/aggro? Villains wont have enough low sc to bluffcatch vs?

PokerStars - $28.78+$1.22|15/30 NL (2 max) - Holdem - 2 players
Hand converted by PokerTracker 4

SB: 1,349 (VPIP: 68.11, PFR: 48.90, 3Bet Preflop: 20.00, Hands: 206)
Hero (BB): 1,651

SB posts SB 15, Hero posts BB 30

Pre Flop: (pot: 45) Hero has 3 4

SB raises to 60, Hero raises to 165, SB calls 105

Flop: (330, 2 players) A 7 4
Hero bets 165, SB calls 165

Turn: (660, 2 players) Q
Hero checks, SB bets 290, Hero calls 290

Why did you 3bet pre? Isn't this the kind of hand you want to see a cheap flop with?

Yes, probably not good to have this as default in your range but can do it sometimes.

easy fold. he's probably calling PF with medium strong and suited Aces + some stronger Kings and Qeens.

3bet pre with these type of hand is good enough to 3bet people who got Ft3b 80% or more. villain with these stats it's easy to exploit by "3bet for value" (JTs+, A7o+, A5s+, K8o+, K8s+, Q9s+). i don't like 3betting every small suited connector againts opponents who just flatting 1/2 of your 3bets.

Pre seems fine. Flop is clear cbet.
I think x/c the turn is really bad. We dont bluffcatch on turn, since there are river and basically every river gonna bring overcard .So even if he has hand like QT he is in good shape. I think it is either bet and be ready for stacking on river or just giving up!

+1. And if I do so, I'd probably bet this turn, not chk/call.

I dont see what the point of barreling turn is w bottom pair. Doubt you are folding out any better hands. So i assume you wanna 3 barrel bluff it. If you 3 barrel bluff bottom pair then you must have a really unbalanced barreling range w way too many bluffs

First look at villain's positional preflop stats - how often is he minrasing button? 3-betting as a bluff makes sense if he is opening really wide on the button.
Flop is very dry. I will make a smaller c-bet (something like 1/3 of the pot).
What is your history with this player? If you always bet the flop and than give up, villain can simply float you profitably with any two cards. Without any specific gameflow information I would fold turn (especially after making bigger c-bet).

You said he floated a lot : so whether he's got the best hand, wheter he's gonna bet if you check and I don't like bluffcatching here on such a bord with a card to come (so Villain can realize his equity).
If he's floating a lot I'm probably firing the turn too.

"If you 3 barrel bluff bottom pair then you must have a really unbalanced barreling range w way too many bluffs "
I try to adjust to what I see ; interset in balancing against a fish?

If villain is "floating" a lot, you should bluffcatch(check-call turn and almost any river), not turn pairs into bluffs on DRY boards(obv you can barrel bottom pair if you have enough bluffcards to come on drawy boards). Here i didnt have a sample on how he plays in 3b pots, so i wasnt sure if him floating in a single raised pot translates to floating here also.
Villain wasnt a fish as you can see from stats.