We analyze fusion cross sections induced by the 6 He halo projectile in the framework of the double-folding São Paulo potential, which has already been shown to be a reliable potential for the analysis of fusion cross sections induced by stable weakly bound nuclei. The results show that the fusion cross sections of 6 He+ 209 Bi, 238 U, 64 Zn are suppressed at energies above the barrier when compared with coupled-channels calculations that do not take into account the projectile breakup, whereas they are in agreement with the calculations at subbarrier energies. The results for the 6 He+ 209 Bi system are contradictory to those reported previously.