We propose a self-organization scheme for cost-effective and load-balanced routing in multi-hop networks. To avoid overloading nodes that provide favourable routing conditions, we assign each node with a cost function that penalizes high loads. Thus, finding routes to sink nodes is formulated as an optimization problem in which the global objective function strikes a balance between route costs and node loads. We apply belief propagation (its min-sum version) to solve the network optimization problem and obtain a distributed algorithm whereby the nodes collectively discover globally optimal routes by performing low-complexity computations and exchanging messages with their neighbours. We prove that the proposed method converges to the global optimum after a finite number of local exchanges of messages. Finally, we demonstrate numerically our framework's efficacy in balancing the node loads and study the trade-off between load reduction and total cost minimization.