This paper considers the problem of the dynamic router node placement (dynRNP) with weighted clients in wireless mesh networks (WMNs), in which both mesh clients and mesh router have mobility, and mesh clients can switch on or off their network access at different times. The main objective of the conventional dynRNP problem is to maximize both network connectivity and client coverage, i.e., the size of the greatest subgraph component of the WMN topology and the number of the clients within radio coverage of mesh routers, respectively. Furthermore, this paper considers a more complicated dynRNP problem in WMNs, in which each client is associated with a weighted value (i.e., the mesh clients with higher weights values are served with larger priority), so that the two objective measures are redefined with consideration of clients' weights. We resolve the weighted problem by a bat-inspired algorithm (BA) with dynamic local search selection scheme, which simulates the echolocation of bats to find the optimal solution. Finally, the performance of the proposed BA is compared with the original BA and PSO, and the effects of weights are analyzed.