Playing KK heads up

[TaintedRogue]

The blinds are 200/400 and I've got about 14.5K, putting me in the top 15. UTG+1, a solid player opens for 1200 and it's folded to me in the UTG+3 seat.
I decide to raise in an effort to ensure it's heads up and make it 2400 to go and everyone folds to UTG+1 who calls.
So we've got 5K plus the antes in the pot.
Flop: Th,8h,3d
Opponent bets 2400. He has approximately 9k left after making the bet.
He could have open/raised with 88 or TT, JJ-AA, but I don't see him being making this move with AK, AQ unless they're both hearts. I don't see him open/raising for 3x BB with less than AQ.
So, how do you play it to confirm he has a set or AA and fold your Kings before you lose almost all of your chips?
I tilted and re-raised the flop, making it 8K to go and he went all in & I called and he had AA and I'm crippled with about about 3.5K left.
If I just call his flop bet, I get no info and he can try and steal again on the turn, so I think I have to raise, and probably the best move was raising the size of this bet, 2400.
But then, he doesn't have to go all in. He can just call and bet out on the turn again.

[Simplistic]

i either like raising flop 3x his bet, pushing, or calling then pushing any non A turn.