Excitation functions of quasielastic scattering at backward angles were measured for the weakly bound 6 Li and 7 Li projectiles on a 64 Zn target at energies around the Coulomb barrier. The corresponding barrier distributions were derived from the experimental cross sections. The experimental data were analyzed within the coupled-channel model using a double-folding potential as the bare potential. Inelastic excitations of the target, the 7 Li first-excited state, and 6,7 Li resonant state(s), corresponding to sequential breakup, were included in the calculations. The comparison between the data and coupled-channel predictions shows that the effects of channels not included in the calculations, such as direct breakup and transfers, are much larger for 6 Li than for 7 Li.