We have measured the elastic scattering of the weakly bound 6Li on the ^116,112Sn targets, at energies close to the Coulomb barrier. The energy dependence of the interaction potential has been investigated by two different methods and the presence of the breakup threshold anomaly is observed. We have also derived the total reaction cross sections for the above systems and compared them to those of other systems with halo, weakly bound, and tightly bound projectiles on targets with similar masses. The reaction cross sections are largest for systems with halo nuclei, then the systems with no-halo weakly bound nuclei, and the smallest cross sections are those for tightly bound systems.