  We present the results of photoionization modeling of nine weak MgII (W_r<0.3
Ang) quasar absorption line systems with redshifts 1.4<z<2.4 obtained with the
Ultraviolet and Visual Echelle Spectrograph on the Very Large Telescope. These
systems have been chosen because they provide access to a regime of red-shift
space that previous weak MgII studies have not looked at. The densities,
metallicities, Doppler parameters, and column densities of these systems are
compared to those of other weak MgII systems at lower redshift. There is no
significant statistical variation in the properties of the absorbers over the
redshift range 0.4<z<2.4. The number density per unit redshift is known to
decrease for weak MgII absorbers between z~1 and z~2 by a greater amount than
predicted from cosmological effects and changes in the extragalactic ionizing
background alone. We suggest that, because the physical properties of the
absorber population are not seen to change significantly across this range,
that the evolution in dN/dz is due to a decrease in the activity that gives
rise to weak MgII absorption, and not due to a change in the processes that
form weak MgII absorbers. The presence of separate, but aligned (in velocity)
low and high density clouds in all single cloud weak MgII absorbers provides an
important diagnostic of their geometry. We discuss possible origins in dwarf
galaxies and in extragalactic analogs to high velocity clouds.
