[ QUOTE ]
[ QUOTE ]
I really hate not betting the flop on hand 1.

There are 4 Aces, 9 hearts, and 8 non heart cards that would pair the board.

[/ QUOTE ]

I didn't like the flop of course, but these are my reasons to check the flop

1) I want to keep the pot as small as I can.
2) I want him to think I have AK
3) I'm not that afraid of the free cards, I don't think he called a raise and a reraise with an A, possible AK and maybe AQs; but since I have KK, I think he has some pair or maybe called with suited connectors. And even if he have TT I'm not that afraid of the straight since I have 2 of the K.

[/ QUOTE ]

The range you gave includes JT, 9T, as well as 4h5h, 5h6h, 6h7h, 7h8h, KhQh, KQ, AK, AQs. I don't see why you're not afraid of giving free cards.