On the flop, you make a potsized bet. Thats good.
On the turn, you bet about two thirds of the pot, leaving you with about half a pot-bet left. I myself would have bet slightly more, about the size of the pot (say $20), having only $20 left in my stack after this. By doing so, I know for sure that
a) Any drawing hand will bnever get correct pot-odds to draw, even considering any implied odds of me paying of an bet on the river.
On the river, since I would only have $20 left and the pot would be $80 after my opponent bets, it would be correct to call if I think he blussf more than one out of five times.
In the scenario that you are describing, you have to call if you think your opponent bluffs more that one out of four times (roughly). If you think that he bluss that often - call.
I would have folded - he played good.