This board is very wet so there is plenty of value to be had by bombing it on the flop. Their ranges are inelastic for the most part, meaning they are either folding or calling, and your bet size (unless you shove) doesn't really matter for the most part, meaning we want to make it really big. This is the same reason we don't want to bluff cbet in this spot and we should just give up with our air.
As for the turn, check/calling puts us in an awkward position, not to mention it caps our range and basically screams, "I don't have the flush." Ideally, we'd like to bet for value on the turn against non-flush hands, disguise our range, and also give ourselves an opportunity to bet/fold should they come over the top.
As played, we kind of opened the door to let villain bluff us and checking doesn't help us narrow his range. If we bet turn and only get called, then we might even be able to go for thin value on the river, or check/fold river as he will likely check back the river with all non-flush made hands since most live players don't valuebet the river well.
Thank you Tecmo for the detailed response. I agree with everything you said. Afterwards I thought about bet/folding, actually I thought about it at the time but disregarded it because I had been losing every pot so I lost all of my confidence.
And definitely bet more on the flop!
Bet on flop needs to be larger, pot imo, and you need to barrel the turn. If you didnt check to induce because you feel a weaker hand would fold to a turn barrel (barrelling is more +EV) then your check is very bad and you turn your hand pretty much face up (non flush draw). I heart draw is a small part of villians flop calling range so you shouldnt be affraid.
Hahahaha, I know every hand it's different and that's what helps me through it. I just remember that I could get the nuts this time. but lately that hasn't been the case. The worst part of it is that you start questioning EVERY decision you're making.