  Recently, it has been shown that the change of resonance widths in an open
system under a perturbation of its interior is a sensitive indicator of the
nonorthogonality of resonance states. We apply this measure to quantify
parametric motion of the resonances. In particular, a strong redistribution of
the widths is linked with the maximal degree of nonorthogonality. Then for
weakly open chaotic systems we discuss the effect of spectral rigidity on the
statistical properties of the parametric width shifts, and derive the
distribution of the latter in a picket-fence model with equidistant spectrum.
