Weighting function for output error IIR filter design I noticed, when I try to fit filter coefficients to a given complex transfer function with the output error method, implemented for example in the MATLAB function invfreqz.m, I get way better results when I use a weighting function that drastically emphasizes the lower frequencies, for example $1/(2\pi f)$. 

Can anybody explain or give me a hint in the right direction, why emphasizing the low frequencies in the weighting function gives so much better fitting results?

My frequency vector is logarithmic, in case that makes a difference and I try to get the best fit for "relatively simple" transfer functions with a very low filter order.
The reason for the worse fit at low frequencies (without additional weighting) is the low density of frequency points at low frequencies due your choice of a logarithmic frequency vector. I'm pretty sure that you will get a better fit at low frequencies if you choose a (more) linear frequency grid.