I'd just go ahead and raise it on the flop to stack worse sets and get draws in. If the flop was mono I think there's more merit to calling. Turn call is fine with our re-draw, river sucks and I'd just check down and hope we are up against 22/77.

line seems pretty good to me. Stacking of 77 and 33 is better because we do not block Top Pair hands which can raise otf.
So nh imo!

Best regards

Pre: Standard.

Flop: Happy to bet this multiway for sure, I don't like flat calling the reraise though when we have the nuts but there are a ton of cards that reduce the value of our hand on the turn. If we reraise here we almost certainly stack undersets where if a bad card comes on the turn these hands will likely slow down. By reraising we also get value from his draws here, of which there are a lot of. I wouldn't expect villain to be raise folding here very often at all so I see no reason to play it slowly.

Turn: When we call flop and the flush card hits then I like flat calling here.

River: When villain checks this river we have two options, check and take our showdown value or turn our hand into a bluff with a substantial bet. I think we have enough showdown value here to check back so I like your line here too.

I would prefer a larger bet size on this flop texture around 15c. It's unlikely we're ever bluffing when we c bet here so they're either coming along or they're not, betting bigger won't affect their continuing range by any real degree.

Once we get raised, even though many micro players will play draws passively, I still want to get the money in for maximum value against the players who will raise a draw. I doubt villain is bluffing with any real frequency so slowplaying is going to end up being a less EV line overall when we miss out on getting all in on the flop or the run out comes as it did in the hand.