I dunno whats best on turn but I would check cuz I think its too thin to bet for value and if we get raised we have to fold which really sucks.

On river his betsize really doesnt look like a bluff and I would expect anything we beat that has value to check it behind. He also doesnt have a lot that hes going to be turning into a bluff, Hands like AQ with a heart seem like theyd get 3 bet PF by this guy. So maybe like 88 with a heart? But again, I often would expect a bigger bet. Id prolly fold

Turn bet is iffy against a competent opponent.We don`t get value from any worse hands and it almost seems like we`re bluffing here.Assuming he won`t fold sets/str8`s/lower flushes to the river bet and probaly raises all of his floats and puts you in a tough spot, you could maybe argue that we can x/f our hand on this turn as nitty as it sounds.

As played x/f river is fine.Hard to think of a hand in his range that gets to the river and is bluffing now.

I think the turn bet is fine.

Villain seems pretty aggressive, and IMO he would probably 3-bet PF overpairs and raise OTF both his FD+OC and his sets/straight (or his slowplayed OP). Also, we got the J of hearts.

When he calls he could have something like 99/88/66, some floating and some baby FD that he is not confortable to raise/broke OTF.

Our range OTT is stronger than his (c-betting on that board with that size is not something you would do ATC), so when we bet the turn that way I am not sure he could raise that lightly: we could play all our flushes like that, and he wouldn't.

Also, by checking he could check behind and freeroll his equity, or he could be more inclined to be aggressive.

River is close IMO, since when you bet the flop and the turn but you check the river your range seems pretty capped, so if he has some busted FD he knows that he doesn't have to bet that much in order to bluff you.

I think his AFq OTR is something to consider, but since he did exactly half pot I would be more inclined to fold, while if he bets something like 13 and his AFq OTR tells me something I may call.

EDIT: Actually, I don't think your checking range OTR should be capped, since you are getting more value checking your flushes IMO, but that he may think that it is.

If he has some broadways with K/Q of hearts i.e. I think he calls (sometimes he can raise for sure, but not that often IMO, because if we 3-bet the turn his life sucks).

I am betting also for protection, since I think we are ahead of his range OTT, but he may improve his hand or bluff us more frequently when hero checks.

Last but not least, when we bet the flop and the turn but we check the river IMO he shouldn't bluff that lightly, since (as already said) we can check also with flushes for inducing, even if we can't be sure that villain is capable of realizing that.

When you check the turn, which is your plan? x/f OTT, x/c OTT and x/f on all rivers unimproved? 

IMO is not a good idea, since your perceived range becomes weaker: you let him the opportunity to bluff more often and/or realize his equity for free, which sounds bad to me.

Your river fold is fine. Since that flop hits his calling range and so does the turn. If he now would float the flop on the turn a RAISE should have followed. In my opinion he hit his hand on the turn and did not raise to scare you off. Usually an aggresive player will raise your turn bet there because it hits his range so well and also improves alot of his drawing hands which have great equity against a hand like JJ. The half turn bet on the river looks like a value bet cause 88-99 would probably raise on the flop or atleast the turn for information/protection

there are very few floats such as KhQx after the opener cbettet into 2 players.  check calling turn is bad cause he can represent the flush with any 2 cards cause u wouldnt check flush on turn. since there are probably by far more single pair combos in ur opponents range i would just bet for value/to not get exploitet by his bluffs/as semi bluff.

Apparently, betting weak hands into strong ranges is the new "value betting".

Which is our perceived range, in your opinion, for c-betting the flop and betting the turn? Because IMO our range is way stronger than his OTT.

I disagree, but of course I could be wrong.

betting turn is overreping yr hand at these stakes. Standard hand for yr c/calling range.