A thorough study of the energy dependence of the nuclear optical potential in reactions involving the weakly bound projectiles ⁸B, ⁷Be and ⁶Li on the target ⁵⁸Ni and ⁹Be on ²⁷Al is carried out by performing a χ²-analysis of recent measurements of elastic scattering cross sections for energies around and above the Coulomb barrier. For this purpose two different potential types are used: the double folding São Paulo potential and the Woods-Saxon potential. The calculations performed for the energy dependence of the real and imaginary parts of the polarization potentials show that these potentials besides satisfying the dispersion relation, for some nuclear systems the uncertainties on the energy dependence of the polarization potentials allow to conclude that these systems present a behavior consistent with the Breakup Theshold Anomaly. In other cases, due to the large uncertainties, it is not possible to make a definitive conclusion about the anomalies.