30+3: sb constantly min raises me. What cards to take a stand with?

[AA suited]

6 players left at 50/100. He was the #2 stack, i was #4 stack. (but dont remember actual # of chips.)

from 50/100 to 150/300 (when i lost), he was constantly min raising me when i was the bb. from all other positions, i never saw him having bad cards when it actually went to showdown. so i would put him as a TAG.

a couple of times i had pocket pair or 2 broadway cards, i re-raised all in. he folded. then immediately next orbit, he would min raise again.

what's an effective strategy against players like this?

and what cards should i re-raise with? top 40%? top 67%?

[lorinda]

I'll sometimes call the second mini-raise at 50-100 to see if it slows them down, only if I can afford to lose of course.

Later on I treat the mini-raise as if I were on the sb and the blinds are 300-600 and play accordingly.

Lori