We examine the influence of meson exchange currents (MEC) on pion double charge exchange (DCX) using the Weinberg Lagrangian. We calculate the corresponding amplitude for DCX and examine its interplay with more conventional mechanisms of DCX for $^{14}\mathrm{C}$ at incident energies of 10 to 110 MeV and for the Ca isotopes at 35 MeV. The MEC effect includes the pion pole term and the contact term. In comparison to previous estimates, we find smaller but nevertheless non-negligible contributions of these effects to DCX. We stress the fact that the MEC contribution to DCX is strongly A dependent, with its effect in light nuclei comparatively larger than in heavy ones.