This paper introduces a novel approach to identifying and estimating parameters in a model where legislators choose their expressed political ideology based on roll-call votes. We consider various professional connections, including cosponsorship, committee membership, and same-state links, to capture the influence of peers on legislators' preferences in the context of the U.S. Congress. We propose an original strategy to uniquely identify heterogeneous network effects by characterizing a subset of individuals' attributes in the population with a stochastic process where dependence vanishes in the multilayer network space. In particular, we assume that the average interest groups' contributions to state politicians affect legislators' revealed policy positions but are uncorrelated with the unobserved characteristics of other legislators far apart in the network space. We propose a Generalized Method of Moments estimator that incorporates the identifying assumptions and demonstrate its consistency and asymptotic normality. By accounting for the inherent network dependence, our estimator allows for correct inference. Through empirical analysis, we validate our main identifying assumptions and observe strong peer effects within the cosponsorship network and a direct influence of contributors' ideologies on legislators' revealed policy positions. Substantively, we argue that the polarizing influence of money in politics and the echo chamber dynamics created by partisan connections and social multipliers offer a potentially consistent explanation for the observed increase in polarization.