Statistics - comparing goodness of fits

[lorenzo123]

I have sets of weighted empirical distributions E and normal distributions N. Each distribution E_i is associated with (derived from, somehow) an N_i (each N_i has a different mean/std). I need to compare each E_i to its associated N_i, and obtain some measure that would let me say something like "E_1 is closer to N_1 than E_2 is to N_2." In other words, I want a number that establishes how good a fit is each E_i to N_i, and be able to compare (e.g. sort?) these numbers to draw conclusions.

I was looking into the Kolmogorov-Smirnov test (kstest in matlab). Would this test be appropriate? How can
I take weights into account?

Any suggestions?

Thank you!