[en] Real-world multiplex networks are weighted in nature, e.g. transports networks (variation in traffic loads over links), social networks (variation in communication between individuals), etc. In addition, the dynamical behavior of multiplex networks is influenced by the contribution of both local as well as global neighbors to individual network layers and the corresponding neighbors in other network layers. In the present work, we propose a method to compute the intra-layer and inter-layer edge weights of multiplex networks and study the consensus dynamics by analyzing the Laplacian spectra from the perspective of long-range interactions (LRIs) in each network layer. To this end, we extend the Kuramoto model for multiplex networks, consider synthetic multiplex networks with different topological characteristics and an empirical data-set. Our analysis reveals that in the case of LRIs, there is an improvement in the stability of the consensus process in the independent network layers as well as in the multiplex networks. However, depending upon the topology of the network layers being added to the existing multiplex network, the behavior of stability is different. In addition, we study the level of synchronization (R) by analyzing the Laplacian spectra and order parameter () of the Kuramoto model. We find that by adding more layers to the existing multiplex network, the value of R increases at the given timestamps in the case of Laplacian spectra analysis. In the case of the Kuramoto model, the order parameter shows different behavior depending upon the topological characteristics of the network layers being added to the existing multiplex network. (paper: interdisciplinary statistical mechanics)