Bet bet bet bet bet. Please bet.

On the flop he either has a K or he doesn't. If he does he's going all the way, if he doesn't you're getting very little more. Raise big.

Is this full ring? If so you have a UTG raiser who will have ...

AA KK QQ you're behind
AK KQ you're behind
JJ TT you're getting zip out of him
Suited connectors you're getting zip out of him
AQ you may get him to call a few dollars
You can pray for KJ KT or whatever, but that seems pretty unlikely.

As played, bet the river and fold to a solid CR. But please bet the flop and the turn.

I usually raise the flop as well, but since there was another player yet to act, and a flush draw available on the flop I may have gotten too tricky by hoping if I flat called I could get one more flat call and then pop it on the turn. Unfortunately the third player folded, and the turn was an ugly card for me.... I checked behind on the turn to manage the size of the pot since AK, AA, or even KK were reasonable hands for him, and I didn't see any hands that would call that I could beat. I actually think there was a better chance I was ahead if he had bet the turn rather than checked it.

So I checked behind, and now the river brings another ugly card. Now I'm behind to a lot of hands, all in his range of hands.

I ended up checking the river, and he showed 44 and I pulled the pot. I don't think I was getting another dime out of him after the flop call, but I could be wrong...

I completely agree with you having to raise that flop. If he has a K he is not goin anywhere and if he doesnt then you probably not getting much more from him. Also he could have a bigger overpair that might catch up to you.

edit:
and also bet the river. 1/2 pot would be good. An ace or king will call you. I dont think a bigger boat checks the river that often since you checked behind on the turn.