Peter,
Of course, the bottom line is that the k-weight shouldn't affect the values of the parameters Ifeffit finds. If it does, it's a sign that the parameters should not be trusted. Often, this happens when the k-range chosen to fit is inappropriate (extends up into a range where the data is dominated by noise, down into a range where the background is poorly chosen, or across a small edge due to a contaminant, for example). I always test my "final" fits at all three k-weights separately to make sure the values of the parameters stay fairly stable.
--Scott Calvin
Sarah Lawrence College