Ok, I am going to attempt to give me best analysis. Obviously, I am no expert, but...this is how we all learn, right?
I really hate this position. So, first...i'd look at what are we ahead of? I think we are beating any AX (that arent suited clubs), underpairs that havent made a set, and maybe some various weird hands that show up like QJ or some such thing.
We are behind anything that makes a straight, pocket 10's or better, the flush cards, and any set/two pair.
As the hand was played...you are either way ahead or way behind. God, i really hate this situation. This guy could so easily have AK/AQ/AJ and floated you just to put the pressure on. Or, he could have a really mean hand here.
Ok, so me personally...i give it up here. I think that if i decide i want to play till the end, I am going to check raise the river. I'd let the clock tick down and then check. I'd expect a bet and then really fast raise. Of course, all this does is beats the bluff and maybe something like 10's or jj. So, most of the time...like i said, I surrender.
Ok, the problem, as i see it is we basically have no clue what the villain has here. So, i would have think that the check-call would have been much better on the flop than the turn. If you follow that with a nice sized turn bet i think that reps serious strength. If your guy still calls you there...you are probably behind.
I think the other option might be to bet the flop bigger...it says "i have overs and I am ahead...call against the odds
if you would like".
I wouldnt say that your play is bad...because, i have probably done this to myself a million times. Something I am starting to really thing about is "what are the ramifications of my actions?"....or, "how will i play this hand when my opponent does X"?
One of the problems is...you know when you checked turn the villain was going to bet. If you call, it doesnt tell you anything about his hand...so, the question becomes what about the river? Even a re-raise on the tunr might have been helpful. I like thinking to myself these things 1.) what am i ahead of 2.) behind? 3.) what does villain most likely have 4.) how do i find this information out 5.) and most importantly, what do i do if villain makes a move (bets, checks, all-in, etc.)
Its actually really difficult to get into the habit of asking all of those questions and the natural desire is to "just play". It is difficult for me anyway, and, i have been in this exact same spot myself....so, anyway I hope something in my ramblings has helped.