AKs Value raise the river?

1/2 game at poker room, 10 handed, no reads.

Hero is CO+1 and is dealt A[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/club.gif[/img]

Preflop

UTG limps and it is folded to hero who raises. The big blind three bets, UTG calls, and hero caps. Everyone calls. Pretty standard I'm thinking so far.

Flop

K[img]/images/graemlins/heart.gif[/img], 9[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/spade.gif[/img]

BB bets out, UTG raises, Hero 3-bets, BB caps, UTG calls, Hero calls

Is the 3 bet my only play here? Folding is obviously out of the question, and I don't like the idea of going into call down mode just yet, especially when it's quite likely I have the best hand. I think by 3-betting this I force my opponents to define their hands to a certain extent. When BB caps I think there's a good chance I'm beat, but let's see what happens on the turn.

Turn

3[img]/images/graemlins/club.gif[/img]

BB bets, UTG calls, Hero calls

Picked up flush draw, and UTG has slowed down.

River

10 [img]/images/graemlins/club.gif[/img]

BB bets, UTG calls, Hero ????

Is this river worth a value raise? The BB hasn't slowed down yet, so I think it's not unreasonable to think there's a good chance he has KK, 99 or something of that nature. I also thought he could have AK, AA, maybe KQ or a weaker king if he's a complete maniac. The other factor I considered in all of this was UTG padding the pot with what is almost certainly a weaker hand, so even instead of the old risk two bets to win one, I'm risking two bets to win two. Easy raise, or just a call?