We analyse the properties of Mg ii absorption systems detected along the sightlines toward GRBs using a sample of 10 GRB afterglow spectra obtained with VLT-UVES over the past six years . The signal-to-noise ratio is sufficiently high that we can extend previous studies to smaller equivalent widths ( typically W _ { r }  >  0.3 à ) . Over a pathlength of \Delta z \sim 14 , we detect 9 intervening Mg ii systems with W _ { r }  >  1 à  and 9 weaker MgII systems ( 0.3 <  W _ { r }  <  1.0 à ) when about 4 and 7 , respectively , are expected from observations of QSO sightlines . The number of weak absorbers is similar along GRB and QSO lines of sight , while the number of strong systems is larger along GRB lines of sight with a 2 \sigma significance . Using intermediate and low resolution observations reported in the literature , we increase the absorption length for strong systems to \Delta z  = 31.5 ( about twice the path length of previous studies ) and find that the number density of strong Mg ii systems is a factor of 2.1 \pm 0.6 higher ( about 3 \sigma significance ) toward GRBs as compared to QSOs , about twice smaller however than previously reported . We divide the sample in three redshift bins and we find that the number density of strong Mg ii is larger in the low redshift bins . We investigate in detail the properties of strong Mg ii systems observed with UVES , deriving an estimate of both the H i column density and the associated extinction . Both the estimated dust extinction in strong GRB Mg ii systems and the equivalent width distribution are consistent with what is observed for standard QSO systems . We find also that the number density of ( sub ) -DLAs per unit redshift in the UVES sample is probably twice larger than what is expected from QSO sightlines which confirms the peculiarity of GRB lines of sight . These results indicate that neither a dust extinction bias nor different beam sizes of the sources are viable explanations for the excess . It is still possible that the current sample of GRB lines of sight is biased by a subtle gravitational lensing effect . More data and larger samples are needed to test this hypothesis .