NL25 FR: KK against supertight villain

[roll]

The effective stack size here is about 19$

When BB reraises me the first time (to 3$) why do you think there is a huge chance he has AA? I'm seeing his range as JJ, QQ, KK, AA, AK, does anyone disagree with this range? Given this range, there is a 6/(6+6+1+6+8) = about 22% chance that he has AA.

If I just call I let up to two more people in the hand and I go to the flop not knowing where I stand and, as you said, I am playing for set value.

But is a reraise really useless? I.e. by reraising (maybe not min reraising) can't I narrow his range further? For example, given BB's stats you really think he's putting in the 4th raise with JJ, QQ, or AK?

If I can narrow his range to JJ, QQ, probobly not AK, and probobly not AA (if he calls my reraise) OR AA or KK (if he puts in the 4th reraise) then doesn't putting in a third raise serve a very good purpose?
i.e. if I isolate him and he calls I can keep firing as long as the dreaded queen doesn't show up. And if he puts in the 4th raise I can let go of my kings easily either on the flop or preflop.

Assuming everything I'm saying makes any sense, I can go one of two routes:
1) try to play a multi-way pot for a set of kings
2) try to isolate and stack a guy that has a lower pair while trying to avoid getting stacked by aces

How can I decide which way is more profitable?