Villain in this hand seems to be one of the better players at the table but also has a bit of FPS. He calls a lot of raises in position and floats a lot and bets into the pot every time it gets checked around to him. I have $125, he covers. I haven't shown down many hands and my image must be a bit tight. I've raised a few hands preflop but have not made many continuation bets as most pots were multiway.

I raise to $5 in MP with [Kd]. Villain in LP calls, both blinds call.
Flop: [4d][4h]. Blinds check. I check. Villain bets $10. Blinds fold, I call.
Turn: . I check, villain bets $20, I checkraise allin to $110.

My reasoning at the time: "it's very unlikely that villain has a piece of the board, at best he has a medium pair, maybe something like T9dd. His bets smell like another steal attempt, he really doesn't have a hand that can stand a lot of heat, and even if he calls I probably have 15 outs.".
My thoughts now: "What on earth am I representing here except for a bizarrely played AA/KK? If he's any good he's going to look me up with any medium pocket pair here and fold any hands that I would beat anyway."

What do you think?