Raining Aces

I played a 472 hand session on Saturday, during which I was dealt AA 7 times. Now you know where this is supposed to go, being the resigned poker fatalists that you all are. But it's not gonna go there! I did not get cracked every time. In fact, I won every time. Twice I got it all in PF, once against QQ, once against KK. I netted +59.90 with my 7 AA holdings.

I also had KK 4 times, but this is where the story starts to losing it's sunny disposition. Because one of those KK hands single-handedly rendered my session bloody red. I ended up down $10. I'm not whining about the end result, because I fell down a full $50 buy-in within 10 minutes of starting play. Here's the hand that I so badly butchered.

BTN is 29/13/3.3 over 125 hands.

Full Tilt Poker, $0.25/$0.50 NL Hold'em Cash Game, 4 Players
Hero (BB): $53.40
UTG: $34.85
BTN: $105.10
SB: $22.70

Pre-Flop: K K dealt to Hero (BB)
UTG folds, BTN calls $0.50, SB calls $0.25, Hero raises to $2, BTN calls $1.50

Flop: ($4.50) T J 7 (2 Players)
Hero bets $3, BTN raises to $7, Hero calls $4

Turn: ($18.50) 3 (2 Players)
Hero checks, BTN bets $15, Hero raises to $44.40 and is All-In, BTN calls $29.40

River: ($107.30) 7 (2 Players - 1 is All-In)

Results: $107.30 Pot ($2 Rake)
Hero showed K K (two pair, Kings and Sevens) and LOST (-$53.40 NET)
BTN showed 9 8 (a straight, Jack high) and WON $105.30 (+$51.90 NET)

I have to say that it's been quite a while since I've had an overpair get skewered like this. I'm sure that had a strong influence on my play and my apparent confidence that I was in pole position.

But I'm still left with a few questions about what was the right way to play this hand. There are two critical points here, the flop and the turn.

On the flop, Villain raises my C-bet from $3 to $7. Maybe I should I have been suspicious about a small raise. But if anyone tells me that they're folding there, I'd say they're crazy. Because if you fold an overpair to a min-raise (for all practical purposes) on the flop, you're throwing away dough. So I'm either calling or raising. Retrospectively, I think my mistake was not making another raise here. The benefit of my opponent's small raise is that he leaves me with room to make another re-raise without committing myself to the pot. So I could have raised to $17-$20, and given myself a chance to get away if he pushed. But if he doesn't push it in there, what am I doing when a blank hits the turn?

But a part of my villain's range here is a flush or straight draw (or both), so part of my logic was to hope for a blank on the turn and then make a strong move. That's what I ended up doing, check-raising all-in on an off-suit 3. I thought Villain's $15 turn bet seemed largish after making such a small flop raise, so I read it, optimistically, as a semi-bluff.

Maybe this is a worst-case type of situation, with little chance of escaping, but I wonder if anyone has any advice on how to act here.