We verify, in Mn:Zn bilayers, that the Hall conductivity is averaged in a bilayer of non-magnetic or ferro- and paramagnetic materials, as previously reported, with thickness as a weighting factor, and also verify that this can lead to anomalously large Hall coefficients. We extend these results to Ni:Pd bilayers in which the ferromagnetic layer increases the effective Hall coefficient of the non-magnetic layer by a factor of I + chi(m) Finally, we discuss the implications of these results for earlier studies in rare earth films covered with thin palladium layers.