[potamophobia]

From your original post it sounds like the old man plays fairly straight forward. If he has a decent, but vulnerable hand he will bet it. If he has AK or AA in this spot, I think he is betting the flop. If he has TT-QQ I think he will probably check fold. If he has KK, he will probably slowplay it.

When he checks the flop I think you are behind exactly KK. I would definitely bet the flop because you need to figure out what the guy has. Yes, you might not get max value if he has QQ, but you need to find out if he has a good hand now.

On to the turn..

When he bets the turn he could easily have TT-KK, and now its pretty much a guess. I am going to call the bet and see what he does on the river. Most people will not bet TT-QQ on the river because it does have showdown value. If he fires again you might be getting outplayed, but I think you should probably fold.

On a side note, I dont think the old man has any idea you have a king. I would expect anyone with a king to bet the flop in your position. When you call 4th street he is going to be pretty confused to your holding, but he might think it is you with something like TT.

So basically as played I would call the turn, and fold to any decently sized river bet.