[thesharpie]

It's twice as likely he has AK than KK if I calculated correctly... But that's not taking into account he's more likely to raise KK than AK on the flop, and more likely to cap KK against 2 raises preflop.

Lead the flop, if not that at least raise when it's 2 back to you. Not only do you want to push your large equity edge here, if he caps the flop you have more of an idea whether he has KK if he also raises this turn.

Edit: And I don't cap the river the way you played it. I don't want him checking through his AK if he thinks I plan on checkraising him again, but I also don't want to get raised by KK if I lead. It's close between check calling and bet calling.