For emerging resource-constrained sensor networks, energy efficiency and computation simplicity could be as important as precision. Existing terrestrial synchronization protocols have already achieved high precision in radio networks, but none of them perform well in high latency networks like underwater acoustic sensor networks: they either assume instantaneous packet transmission between nodes, or ignore clock drift during synchronization process. By addressing these problems, the recent proposed TSHL protocol provides precise time synchronization for high latency networks. However, due to its high energy and computation consumption, original TSHL design is still not practical in resource-constrained applications such as sensor networks which have stringent constraints on system resources. The main results of this paper are as follows. First, we present a complete mathematical analysis of TSHL which is lack in the original paper. Dominant factors of errors are clarified, as well as communication and computation cost functions. We prove that even with as less as 3 beacon messages, an acceptable precision level can be achieved by increasing beacon messages interval. In this lightweight synchronization, communication and computation cost for the synchronization process are greatly reduced, which is critical for those high latency and resource-constrained sensor networks.