fold kk preflop vs solid player?

hand from the $10 rebuy, avg is 15k, ~700 left

villain is ender555... I can tell he's a solid player, and he also posts at pocketfives.com. He played recklessly at the beginning of the rebuy but tightened up once he built a stack. At one point I raised to 500 (50/100 blinds) with AK UTG after not having played a hand in quite some time (stack = 6000, he has me covered) and he went allin. I folded, very confident he had KK or AA, which he said he did, and that he thought I'd call because he'd been reckless earlier. Pot if I push (obviously it's push or fold) is 40k, I have 17k more to push. With all this information, does he have QQ/AK enough to call?

PokerStars No-Limit Hold'em Tourney, Big Blind is t200 (9 handed) converter

saw flop

CO (t22805)
Button (t16425)
SB (t7275)
BB (t11940)
UTG (t22885)
UTG+1 (t13277)
Villain (t21887)</font>
MP2 (t8294)
Hero (t20353)</font>

Preflop: Hero is MP3 with K[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/club.gif[/img].
<font color="#666666">1 fold</font>, UTG+1 calls t200, <font color="#CC3333">Villain raises to t800</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to t3200</font>, <font color="#666666">4 folds</font>, UTG+1 folds, <font color="#CC3333">Villain raises to t10000</font>