To study the effect of the weak binding energy on the interaction potential between a light exotic nucleus and a target, elastic scattering of ${}^{6}\mathrm{He}$ at 38.3 MeV/nucleon on a ${}^{12}\mathrm{C}$ target was measured at Grand Acc\'el\'erateur National d'Ions Lourds (GANIL). The ${}^{6}\mathrm{He}$ beam was produced by fragmentation. The detection of the scattered particles was performed by the GANIL spectrometer. The energy resolution was good enough to separate elastic from inelastic scattering contributions. The measured elastic data have been analyzed within the optical model, with the real part of the optical potential calculated in the double-folding model using a realistic density-dependent nucleon-nucleon interaction and the imaginary part taken in the conventional Woods-Saxon (WS) form. A failure of the ``bare'' real folded potential to reproduce the measured angular distribution over the whole angular range suggests quite a strong coupling of the higher-order breakup channels to the elastic channel. To estimate the strength of the breakup effects, a complex surface potential with a repulsive real part (designed to simulate the polarization effects caused by the projectile breakup) was added to the real folded and imaginary WS potentials. A realistic estimate of the polarization potential caused by the breakup of the weakly bound ${}^{6}\mathrm{He}$ was made based on a parallel study of ${}^{6}\mathrm{He}{+}^{12}\mathrm{C}$ and ${}^{6}\mathrm{Li}{+}^{12}\mathrm{C}$ optical potentials at about the same energies.