To further our understanding of the influence of weakly coupled channels on the distribution of Coulomb barrier heights, we have measured transfer cross sections for 20Ne ions backscattered from natNi, 118Sn, and 208Pb targets at near-barrier energies. The Q value spectrum in the case of 208Pb target has been determined too. The transfer channels appear to be especially important for 208Pb, whose double-closed-shell nature leads to a relatively low level density for noncollective inelastic excitations.