ajo

Flop... call flop/raise turn clearly fine

Turn... very bad card,I would say you are pretty much at the bottom of your range that wants to see SD at this point...so no need to raise everything

River...if he bets Im folding... His range includes super many two pair+ hands,Tx,even hand like KQ and overpairs are totally legit (he didnt cap them preflop),out of the range that you beat there is only hand like KJ or highly unlikely A9 that you bet.I would say most regs(especially weakish ones will not turn such hands into bluffs and will check them)...also at this point you are at the bottom of you range and certainly fine to fold

when he check I would say it mostly is A9,KJ and maybe Qx or overpairs and obviously Tx that wants to c/r.
I would assume this....out of this range Qx and overpairs are not that likely due to I think most decent players will valuebet them as it makes not too much sense to check them behind...still weaker players may have some of these there. I also dont think that c/r is very likely since you hand looks very much like the one that wants to see cheap SD,still he can have a few of these.
Then if he has A9 Im pretty sure he is not going to c/c as its clearly super bad but will c/f. So the only hand that may be there is KJ which I also think that has to be reduced since I would say he doesnt c/c it all the time, I say he cbets it or even just plays c/f.I think c/f is totally fine and betting it would be pretty much turning it into a bluff.

So to valuebet here and play b/f you need about 50%+ equity vs his non folding range... that includes some Tx,some better pairs(like Qx) and occational KJ that will call.... I think there is no need to bet it since its at the bottom of our range,I would say we have a few better hands at this point(like AQ,KQ,maybe QJs) that we will bet...so I totally like your check