In practical wireless mesh networks (WMNs), gateways are subject to hard capacity limits on the aggregate number of flows (in terms of bit rate) that they can support. Thus, if traffic is routed in the mesh network without considering those constraints, as well as the traffic distribution, some gateways or intermediate mesh routers may rapidly get overloaded, and the network resources can be unevenly utilized. To address this problem, in this paper we firstly develop a multi-class queuing network model to analyze feasible throughput allocations, as well as average end-to-end delay, in heterogeneous WMNs. Guided by our analysis, we design a Capacity-Aware Route Selection algorithm (CARS), which allocates network paths to downstream and upstream Internet flows so as to ensure a more balanced utilization of wireless network resources and gateways’ fixed connections. Through simulations in a number of different network scenarios we show that the CARS scheme significantly outperforms conventional shortest path routing, as well as an alternative routing method that distributes the traffic load on the gateway nodes to minimize its variance.