The production of alpha particles in the 6Li+28Si reaction was studied at near-barrier energies. Angular distributions were performed at four bombarding energies, namely, 7.5, 9, 11, and 13 MeV. The distributions were characterized by a Gaussian shape, which was integrated in order to obtain alpha-particle cross sections. Our results were compared with previous data of 6Li scattering on various heavier targets and found to exhibit a universal behavior. Present continuum-discretized-coupled-channel calculations support the obtained data. The consequences of the systematic behavior of the alpha-particle production on the unusual behavior of the imaginary potential observed previously in elastic scattering of weakly bound systems is discussed.