The min-raise in my experience usually means one of two things.
1) Extreme strength
2) Extreme weakness

I don't play full ring online, but I know in 6-max, I am raising the min-raise a good portion of the time with KK here. (This of course depends on the villain and my table image also) If I face a 4-bet, I will go away because only complete lunatics 4-bet with air.