Could you get away from AA in that spot?

It isn't fishy at all to play K♠:Q♠: that way, and with K♠:3♠: it would be excellent... If you had AK here, I'd say fold for reasons (too long to state here) that has to do with balancing. With AA you are on your own as played.

I'd not reraise on the flop, I'd call. This makes it much harder for villain to play, since his original plan was probably to get it in on the flop whether he has a draw or not.

With a call on flop aren't we inviting the CO too?

Hmmm, admittedly, I didn't notice the CO. My bad.

Nitrol's astute observation that there are more people in the pot renders my first post useless. But I am still calling. The rationale is that BB is now very unlikely to bluff with air (K♠:Q♠: is not air) or be value raising too lightly. I'd call and be very careful on the turn.

Trying to extract money from two players when you lag one and lead one in ranges is very hard. I mean you'd wish to extract money from CO (whom you lead) and at the same time avoid getting done over by BB (whom you lag). This is easier said than done.

If BB is not on air, isn't it better to try and extract maximum from his Kx hands?

I include those in "not value raising too lightly".

I think you played this fine.