I know but in this hand I think it is ok.
If we underbet and villain folds, it is ok. If he calls with worse, excellent. If he calls with better, we probably lose the minimum since by x/c we probably will lose more. Villain probably doesn't raise our bet as a bluff so we can fold and not worry about it. The only scenario where this is not so good is if villain really raises us OTR with weaker holding but I would say this is so unlikely that we don't have to worry about it.
If we check/call:
Well, it is unlikely that villain goes for 3 streets with weaker hand so he probably checks those behind and we just missed some value.
So again, if we bet small we get thin value from that part of villains range that would have checked behind and if he has a better hand here we risk only 10bb.
I think we have provided you with a list of good reasons to do this and only thing you have done is ask questions and try to make this line look bad, which has failed imo. Is it your turn now to write a wall of text and tell us why check calling is ultimately the best line here?