Will start off with the hand.. H raises to $15 over UTG limper with AhJc, CO and BTN (Old nits) call, UTG calls

Flop ($60): J76hhc
Check, H $40, fold, BTN minraises to $80 with $80 behind, UTG folds, H tank folds face up

Old guy says later “good fold.. set”

My question is: is it better to exploitatively bet 1/3 pot in these spots to

a) get called by worse hands, and
b) snap fold if these guys raise because they just never do it with worse?

If they just flat flop and turn is a blank, we can then go larger if need be.

I know holding Ah makes this even more of a fold, but let’s assume we have any Ax here. I doubt it changes anything vs these guys because they don’t raise Axhh OTF.

If you bet nothing and he bets on the flop, you could fold and save even more money.

It might not be a bad strategy if you knew the villain would never bet out without better than TPTK. For even weak tight players, you're leaving money on the table if they will call with less that TPTK. Also don't forget there was another player in the hand. He had outs if you decided to just bet small or nothing.

Stop folding face up to old nits. It's not like they will start bluffing you and you can thus get them to overplay bad hands. It's just showing off and giving the rest of the table free information.

As for the rest, what venice said, and obvious snap fold is obvious.

I don't like the 1/3 pot bets in multiway spots. It's too likely that you'll get action from one or more players, especially on these wet boards. Your bet size was fine. You are often good on these flops, but there are a lot of bad turns here, so checking is bad. There are plenty of draws you can get value from here.

Folding here is probably good. Don't fold face up unless you have a specific reason for doing so. At low stakes there is almost no reason to show a tight fold. All this will do is cause some opponents to adjust by opening up their bluffs. Since most low stakes players don't bluff nearly enough, I'd like to keep it that way.