We have performed CDCC calculations for the $^{6}$Li + $^{59}$Co, $^{144}$Sm and $^{208}$Pb systems, to investigate the dependence of the relative importance of nuclear and Coulomb breakup on the target charge (mass) at near barrier energies. The calculations were in good agreement with the experimental elastic scattering angular distributions for these systems and then, their predictions to the nuclear, Coulomb and total breakup were investigated. Although the relative importance of the nuclear breakup is, as expected, larger for lighter targets, this effect is not very pronounced. We also investigate a scaling of the nuclear breakup with the target mass and we compare the predictions for the integrated total breakup cross sections with experimental fusion cross sections at similar energies.