NL5 check behind or play for value?

You didn't limp, it's an overcall (correct me if I'm not right). You can call it of course, cause it's a multiway and this kind of hand is playing well postflop if it hits a draws.

I don't like how you played this hand postflop. Why did you call bet on flop? You are drawing to 3 outs, I think that we can eliminate 9 cause it improves a flush draw. You need 15:1 pot odds to call this bet, you have only ~4:1, it's easy fold for me.

As played: I'm raising turn, you don't want to see another heart, or a paired board. Someone should pay here anyway.

Sorry, you are right, it was an overcall.
I played it postflop because I am used to players just giving up after c-betting their hand when they did not hit. So in this position I could from time to time bet myself on the flop and take down the pot (or check behind again and hope for a nice river). Also, I would count a T or J (no hearts) as good outs, as opponents might easily have AK, lower pairs or flushdraws. I see that this is still not enough in pot odds, and the implied odds don't make up for this, so possibly a leak.

On the turn, I do not want to ship it directly, because this might still scare ppl off overpairs, lower 2-pairs, flushdraws etc. And of course I should balance a bit and not play check/call with 2pairs, but shove with nuts (though I am not sure whether balancing is needed). So, with this potsize I intend to just call and ship it on almost any river. My question was actually more directed to the river, and whether I should change the plan and just check behind on a paired flop, and how to play on a flush-draw flop. But thanks for your suggestion, I think i really should have given up on the flop:-)

edit: what I actually wanted to say: I used equilab and gave my opponent on MP the loose starting hand raising chart- hands. I think that most players would cbet here 80% of the range(100% if there were no other caller), because they picked up something on the flop, and because the Q makes it a good flop to bet(or am i wrong here). Turn then is an improvement for most hands, and a second barrel/valuebet is also reasonable for most hands.
With the range
55+,AQs,ATs-A9s,KJs+,QTs+,J9s+,T8s+,97s+,87s,76s,65s,AQo,ATo,KQo for the aggressor, and a bit tighter for the caller, I am ahead on the turn by
83%, and 75% on the river. Is the range reasonable?

Hello farbwenz,

Definitely rather a fold on the flop cause you don't have the implied odds there but otherwise raise the turn and protect your hand! Ship da money!

Best Regards.