  We estimate the mean dust-to-gas ratio of MgII absorbers as a function of
rest equivalent width W_0 and redshift over the range 0.5<z<1.4. Using the
expanded SDSS/HST sample of low-redshift Lyman-alpha absorbers we first show
the existence of a 8-sigma correlation between the mean hydrogen column density
<N_HI> and W_0, an indicator of gas velocity dispersion. By combining these
results with recent dust-reddening measurements we show that the mean
dust-to-gas ratio of MgII absorbers does not appreciably depend on rest
equivalent width. Assuming that, on average, dust-to-gas ratio is proportional
to metallicity, we find its redshift evolution to be consistent with that of
L^star galaxies from z=0.5 to 1.4 and we show that our constraints disfavor
dwarf galaxies as the origin of such absorbers. We discuss other scenarii and
favor galactic outflows from ~L^star galaxies as the origin of the majority of
strong MgII absorbers. Finally, we show that, once evolutionary effects are
taken into account, the Bohlin et al. relation between A_V and N_H is also
satisfied by strong MgII systems down to lower column densities than those
probed in our Galaxy.
