In foundational models of network formation, the mechanisms for link formation are based solely on network topology. For example, preferential attachment uses degree distributions, whereas a strategic connections model uses internode distances. These dynamics implicitly presume that such benefits and costs are instantaneous functions of the network topology. A more detailed model would include that benefits and costs are themselves derived through a dynamic process, which, in the absence of time-scale separation, necessitates a coevolutionary analysis. This paper introduces a new coevolutionary model of strategic network formation. In this model, network formation evolves along with the flow of benefits from one node to another. We examine the emergent equilibria of this combined dynamics of network formation and benefit flow.We show that the class of strict equilibria is stable (or robust to small perturbations in the benefits flows).