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 distribution, unevenly network congestion may arise and some gateways may rapidly get overloaded, which causes a significant reduction of the 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 contentionaware link costs, achieving throughput improvements of up to 210% in the considered network scenarios.