Previous work has shown that genetic diversity at a neutral locus is affected by background selection due to recurrent deleterious mutations as though the effective population size Ne is reduced by a factor that is calculable from genetic parameters such as mutation rates, selection coefficients, and the rates of recombination between sites subject to selection and the neutral locus. Given that silent changes at third coding positions are often subject to weak selection pressures, it is important to develop similar quantitative predictions of the effects of background selection on variation and evolution at weakly selected sites. A diffusion approximation is derived that describes the effects of the presence of a single locus subject to mutation and strongly deleterious selection on variation and evolution at a partially linked, weakly selected locus. The results are validated by computer simulations using the Ito pseudo-sampling method. We show that both nucleotide site diversity and rates of molecular evolution at a weakly selected locus are affected by background selection as though Ne is reduced in the same way as for a neutral locus. Heuristic arguments are presented as to why the change in Ne for the neutral case also applies with weak selection. As in the case of a neutral locus, the number of segregating sites in the population is poorly predicted from the change in Ne. The potential significance of the results in relation to the effects of recombinational environment on molecular variation and evolution is discussed.