  We present results from a survey of weak MgII absorbers in the VLT/UVES
spectra of 81 QSOs obtained from the ESO archive. In this survey, we identified
112 weak MgII systems within the redshift interval 0.4 < z < 2.4 with 86%
completeness down to a rest-frame equivalent width of W_r(2796) = 0.02A,
covering a cumulative redshift path length of deltaZ=77.3. From this sample, we
estimate that the number of weak absorbers per unit redshift dN/dz increases
from 1.06 +/- 0.04 at <z>=1.9 to 1.76 +/- 0.08 at <z>=1.2 and thereafter
decreases to 1.51 +/- 0.09 at <z>=0.9 and 1.06 +/- 0.10 at <z>=0.6. Thus we
find evidence for an evolution in the population of weak MgII absorbers, with
their number density peaking at z=1.2. We also determine the equivalent width
distribution of weak systems at <z>=0.9 and <z>=1.9. At 0.4 < z < 1.4, there is
evidence for a turnover from a powerlaw of the form n(W_r) \propto W_r^{-1.04}
at W_r(2796) < 0.1A. This turnover is more extreme at 1.4 < z < 2.4, where the
equivalent width distribution is close to an extrapolation of the exponential
distribution function found for strong MgII absorbers. Based on these results,
we discuss the possibility that some fraction of weak MgII absorbers,
particularly single cloud systems, are related to satellite clouds surrounding
strong MgII systems. These structures could also be analogs to Milky Way high
velocity clouds. In this context, the paucity of high redshift weak MgII
absorbers is caused by a lack of isolated accreting clouds on to galaxies
during that epoch.
