Missed Value bet on river?

[Uppercut]

I had just entered a new .50-1.00 table on Paradise after having my wired Kings snapped by a J8 offsuit hitting a straight on the river on a different table. I get Q3 offsuit in the CO. Everyone limps, so I get to see the flop for free. Just as I am thinking that I never get a great flop from my forced bets, the flop comes K33. Hallelujah!!! Everyone checks to me and I bet out. UTG check-raises me and I three bet it. I discount UTG from having KK because she limped pre-flop. (In hindsight, this assumption was dead wrong, but in a good way.) I am worried however, that UTG might have A3. People on Paradise love to limp with Ax. I am a bit relieved when UTG merely calls my three bet.
Turn card is a 9. (Suits are irrelevant.) UTG checks, I bet out, and she check-raises me again! Once again, I three bet it and she calls. What I am supposed to assume at this point? I am hoping that she has J3 or T3, but those do not seem like hands that anyone would limp UTG with. She can't have K3 because she hasn't been capping my three bets on either the flop or the turn. She could have a pocket pair, but I clearly am demonstrating that I either have a King or a 3 in my hand and she still keeps check-raising me.
River is a rag. UTG bets out. I meekly call. She exposes pocket Aces for two pair. My trip threes are good and I rake a nice sized pot. Question: Did I wimp out on the river, or was this a prudent call on my part?

[Bob T.]

You kept telling your opponent that you had them beat, and they keep betting into you. At some point, you have to give them credit for having a hand. I think that I would have called in on the river here also. I think your opponent overplayed their hand. I would put in my notes, that your opponent plays an overpair very strongly, and maybe give them a lot of action in the future, if an overpair is one of their possible hands, and you can beat an overpair.

[GrinningBuddha]

And this, ladies and gentlemen, is why you raise AA UTG even (especially) in low limit games.

Of course, half the time the person who posts will call anyway (I know you wouldn't Uppercut) and you'll lose an extra SB, but the extra bets you make up from the other cold-callers on your winning hands will more than offset that.

Well played Uppercut.

[Uppercut]

I assume that my opponent did not raise the AA pre-flop because she was UTG and tried to get fancy with a limp re-raise pre-flop. Since nobody raised pre-flop, her cleverness ended up costing her the pot, because I definitely would've folded to a raise pre-flop. This is exactly why I raise AA pre-flop approximately 100% of the time.

[me454555]

I think you played this hand beautifully. If you dont know that you have the best hand for sure, its better to just call than try a value bet that you might loose.