  We present a statistical analysis of the photometric properties and spatial
distribution of more than 2,800 MgII absorbers with 0.37<z<1 and rest
equivalent width W_0(\lambda2796)>0.8\AA detected in SDSS quasar spectra. Using
an improved image stacking technique, we measure the cross-correlation between
MgII gas and light (in the g, r, i and z-bands) from 10 to 200 kpc and infer
the light-weighted impact parameter distribution of MgII absorbers. Such a
quantity is well described by a power-law with an index that strongly depends
on W_0, ranging from ~-1 for W_0<~1\AA to ~-2 for W_0>~ 1.5\AA. At redshift
0.37<z<0.55, we find the average luminosity enclosed within 100 kpc around MgII
absorbers to be M_g=-20.65+-0.11 mag, which is ~0.5 L_g*. The global
luminosity-weighted colors are typical of present-day intermediate type
galaxies. However, while the light of weaker absorbers originates mostly from
red passive galaxies, stronger systems display the colors of blue star-forming
galaxies. Based on these observations, we argue that the origin of strong MgII
absorber systems might be better explained by models of metal-enriched gas
outflows from star-forming/bursting galaxies. Our analysis does not show any
redshift dependence for both impact parameter and rest-frame colors up to z=1.
However, we do observe a brightening of the absorbers related light at high
redshift (~50% from z~0.4 to 1). We argue that MgII absorbers are a phenomenon
typical of a given evolutionary phase that more massive galaxies experience
earlier than less massive ones, in a downsizing fashion. (abridged)
