We present new experimental angular distributions for the elastic scattering of $^{6}\mathrm{Li}+^{120}\mathrm{Sn}$ at three bombarding energies. We include these data in a wide systematic involving the elastic scattering of $^{4,6}\mathrm{He},\phantom{\rule{0.16em}{0ex}}^{7}\mathrm{Li}$, $^{9}\mathrm{Be},\phantom{\rule{0.16em}{0ex}}^{10}\mathrm{B}$, and $^{16,18}\mathrm{O}$ projectiles on the same target at energies around the respective Coulomb barriers. Considering this data set, we report on optical model analyses based on the double-folding S\~ao Paulo potential. Within this approach, we study the sensitivity of the data fit to different models for the nuclear matter densities and to variations in the optical potential strengths.