SH Q9s, Two overs + Backdoors vs Flop Cbet

Your overs are quite weak and so are your backdoors. I would usually xr backdoors that have better nut potential so this might be a check/fold for me OTF but I don't completely hate your play.
OTT I would usually barrel when I improve my hand but I'm not sure if this improvement is that great. You turn a gutshot. Td would definitely have been a barreling card and maybe any diamond but maybe not this one.

Hmmm... difficult.

I kinda agree with la55i here, though I also don't have a set check-raising range in this spot. But it makes sense to check/raise stronger backdoors as well.

To argue for your play, Villain makes it very small on the flop, therefore it's not too bad. But I would go MUCH bigger on the turn and bet at least 80% pot. Why? Because I want the foldequity vs. flushdraws and 8x. I also don't think people fold QQ+ on the river. Then, I would give up umimproved. I think that's the cheaper option to try to make it a 2-street hand rather than spewing money on 3.

But, Generally I would have called the cbet and tried to float this board for cheap

I like PF call. OTF it´s more bluff than semi-bluff imo. And as it didn´t work, I don´t think we should continue OTT. T of spades doesn´t really change anything. We pick a gut shot, but also lose backdoor flushdraw. I think we should give up after our raise OTF didn´t work, because what he called our raise with will most likely call also bet OTT.