Prolonging network lifetime of wireless sensor networks (WSNs) is a challenging task because of the heterogeneity among sensor nodes inherited from real worlds in forms of different residual energy, transmission speed, transmission range, and nodal traffic. Thus, it is necessary to consider the impact of the heterogeneities when trying to balance the energy consumption in sensor nodes. In this paper, we present a distributed probabilistic load-balancing converge cast tree algorithm (PLCTA) to address the heterogeneity issues in terms of nodal traffic burden and residual energy by dynamically forming converge cast routing trees. For these purpose, a selfish weight assignment approach is easily applied to nodes and able to automatically adjust the weight of each link between a node and its candidate parent nodes using local information. When nodes try to get their own benefit, such as saving energy and reducing traffic burden, they implicitly help construct the load balanced converge cast tree. Simulation results show that our proposed PLCTA indeed improves the routing efficiency through the load balance strategy designed for heterogeneous WSNs and leads to network lifetime prolongation.