In this paper, we investigate the problem of resource constraints in Mobile Peer-to-Peer Wireless Sensor Networks (MP2P WSNs). We propose a scheme to load share tasks among peer sensor nodes, taking into account both their computational capabilities and networking conditions. Experiments to evaluate the performance results were conducted over real Tmote Sky sensor testbeds. We demonstrate that significant performance improvements in terms of latency can be achieved for a MP2P WSN by considering both load and network constraints, and we argue that, when ignoring the latter, the performance of MP2P computing in the application overlay could be severely impacted.