Why do this with AK? Because he can trap you with AQ or maybe AJ. Just look at your thought process now.
The bigger question is why the hell he would risk his whole stack with KK on this board, and what purpose that serves. If you're loose enough to look him up with AQ (sounds like you're pretty close to doing so), then villain should have picked up on this and should know that he should expect to get called fairly often.
As for your strength tell, he could easily be using reverse tells
. They say not to bank your hand decisions on tells, and I think this could be a perfect example.
A few more things.
For one, are you actually on the button or in the blinds? ie how do you check-raise an LP raiser if you're on the button?
Also, calling the flop is also a viable option - one that I actually like better. This is basically classic wa/wb, as villain either has AK/AA and has you crushed, or he's got QQ-KK/KQ/AJ or something similar and you have him crushed. In those spots it's often good to play your hand passively to keep the pot small because most times you're not getting a lot of action from a hand you have beat, so there's no use in betting it strong.
I just think we have to take a step back here and realize that we're about to stack a 'very tight' player with AQ on an A33 flop. Even if it is a decision between AK and KK, we're more likely to see AK since there are more combinations of the hand (16 vs 12 I think).