We revisit echelle spectra (spectral resolution R 40,000) of eight gamma-ray burst (GRB) afterglows to obtain the incidence (dN/dz) of weak intervening Mg II systems at a mean redshift of 〈z〉 = 1.5. We show that dN/dz of systems having rest-frame equivalent widths 0.07 Å ≤ WrMgII < 1 Å toward GRBs is statistically consistent with the incidence toward quasi-stellar objects (QSOs). Our result is in contrast to the results for Mg II systems having Wr ≥ 1 Å, where dN/dz toward GRBs has been found to be larger than toward QSOs by a factor of ≈ 4. We confirm the overdensity albeit at a factor of ≈ 3 only. This suggests that any explanation for the GRB/QSO discrepancy, be it intrinsic to the absorbers or a selection effect, should be inherent only to the galaxies that host strong absorbers in the line of sight to GRBs. We argue that, of all scenarios that have been proposed, lensing amplification is the one that could explain the strong Mg II enhancement while allowing for no significant enhancement in the weak absorbers.