The curve fitting algorithm in the Transmission Line and Cable Constants program is based on a weighted least squares analysis technique. This is a mathematically solid method to solve an over-determined set of equations (i.e. you have 200 pieces of data over the frequency range, but need to derive 10 parameters for a 5th order approximation).
Specifying a higher weighting factor at a given frequency (or over a range) will instruct the curve fitting algorithm to consider these frequencies to be 'more important' so that the pole/zeroes will be placed such that the error in this range is reduced. This is most often used to increase the accuracy at the fundamental frequency so that the steady state error on the line will be very small, even though the overall error is less then the error you specify. For example, you may want to have an extremely good fitting at the fundamental frequency (as this will affect the fundamental frequency load flow), in which case the Least Squares Weighting Factor at F0 can be increased so as to emphasize this data set.
Generally the Least Squares Weighting Factor, 0 to F0 and Least Squares Weighting Factor, F0 to Fmax parameters can be left as 1.0, and a higher value (say 100 or 1000) can be used for the Least Squares Weighting Factor at F0 if you require a very good fundamental fit. In any case, the iterative curve fitting algorithm will ensure that the maximum error at any frequency is less then the Maximum Fitting Error for Surge Admittance and Maximum Fitting Error for Propagation Func. parameters.