Fusion cross sections were measured for the ^6,7Li + ²⁷Al, ⁶⁴Zn systems, at energies above the Coulomb barrier, in order to study the influence of the break-up of stable weakly bound nuclei on the fusion process. The analysis was completed by the inclusion of the data of fusion induced by ⁹Be and the strongly bound ¹⁶O and ¹¹B projectiles on the same targets. The fusion excitation functions have similar behavior for all projectiles incident on both targets and they show no signature of fusion hindrance.