Wireless mesh networks are primarily used to provide Internet access by sharing the Internet connections of a limited number of gateways. If traffic is routed in the mesh without considering load distributions, unevenly network congestion may arise, or some gateways may rapidly get overloaded because are selected by too many mesh nodes. This results into a significant reduction of overall network capacity. To address this issue, in this paper we firstly develop a queuing network model that accurately predicts the residual capacity of paths in heterogeneous mesh networks, and precisely identify network bottlenecks. By taking advantage of this model, we design a novel Load-Aware Route Selection algorithm, named LARS, which improves the network capacity. This objective is obtained by allowing each mesh node to distribute the traffic load among multiple gateways in order to ensure evenly utilization of Internet connections. Simulation results show that LARS significantly outperforms shortest path routing using contention-aware link costs, providing up to 210% throughput improvement in some network scenarios.