Well the way it played out wasn't great for you and now you know that. As I might have thought, villain had the OESD with an overcard. If you saw the 2h or 7h fall you were surely going to double up off him. It's very likely that any other heart may have killed your action, but it seems to me that if either of these cards fell villain just wouldn't be able to get away from his straight. The Kh was also probably a great card if it had fallen instead of the Kd, so it turns out that 3 cards would have helped you completely break your opponent and he may have bluffed off the rest of his chips with top pair chasing that straight anyway. Unfortunately, the Kd was one of the few cards that totally killed your overcard outs here and reduced the probability of you having the best hand at showdown. You had 15 live outs on the turn and now you have 9 on the river. You also have to consider the (remote) possibility that villain is playing with a flopped set and any heart that pairs the board may no longer be an out for you. This is highly unliklely in most cases, but you have to decide that based on what you know about your opponent and how he has played similar hands against you. This would be a good time to decide between check/call and check/fold based on the size of villains bet. At this point I'm very glad I didn't commit everything on the flop.