Empirical analyses that characterize the mechanisms that mediate spillover effects often do so by relating responses to a treatment, shock, or policy change with a chosen measure of economic proximity, such as geographic distance, technological similarity, trade, or migration flows. Typically, such efforts are based on regressions that associate outcomes with proximity-weighted averages of the treatments received by other units. We show that regressions with this structure measure how the association between one unit's outcome and another unit's treatment correlates with the proximity between the two units. If the proximity measure of interest is associated with other channels that mediate spillover effects, then causal interpretations of such relationships are susceptible to confounding. For instance, if technologically similar firms tend to be geographically proximate, then a positive association between technological similarity and the intensity of the productivity spillovers between firms might arise spuriously. We give conditions under which the effect of a proximity measure of interest on spillover intensity can instead be recovered by regressing outcomes on averages of other units' treatments, reweighted by residualized versions of the proximity measure under consideration. We show that estimates obtained in this manner achieve the optimal rate of convergence and give a resampling procedure for constructing estimates of the associated uncertainty. We illustrate the proposed method with several empirical applications.