Once again some stats/reads on villain would be nice :-).

This seemed like a pretty good spot to barrel for me since he will often fold his draws and if you bet a bit bigger like 6$ it will put him in a spot where he will be playing for his stack and you can still fold to a raise. However, I looked at it in PJ and I would give up on the flop and as played on the turn as well.

Preflop:
Since he raises over 2 limpers I would assume a rather tight range, maybe like 15% RFI and then exclude AA since he doesnt 4bet.

Flop:
On the Flop he will have 40% EQ, I think he raises any set pretty much 100% of the time and calls with JT+,89+,KQ9+,AQ89+,T+:87+ and exluding 66+,KQ98+,AKQJ. He might call with those wraps sometimes or even raise worse, so I just put in a few to balance it. This means that overall he continues 72% of the time, meaning we need to make some +EV turn moves to make up for it. Maybe giving up right here wouldnt be that bad, a Jtx flop just smacks a strong preflop range that doesnt include AA, and all we have is a GSD and backdoorflushdraw.

Turn:

Im assuming that we are rarely getting called and he will either fold or get it in.
He has T+ 32% of the time, if you change his preflop range to RFI25% it only drops to 31%. If you bet 6 in 9,79 you need
x * 9,79 – (1-x) -6 =0
x=38%.

So what else does he have to call on the turn? If he continues with T+,KQJ9+,Q98+ he is at 40%. Now there is the question of how much we make up for it if we bet the turn, villain just calls and we actually win the hand, but it seems pretty damn hard to answer :-).

So I guess I just give up on the flop. We do not have much FEQ here and our implied are pretty low as well, since he wont pay if we hit our A. And a T on the turn is even one of the better turncard, if it is a 5h for example he will not fold his wraps (I assume).

Betting doesnst accomplish much OTT, besides folding out his straight draws which you already block.