Processing uneven data requests is crucial for Low Earth Orbit (LEO) satellites to effectively balance resources. Various multi-hop peer offloading methods have been proposed to address this challenge. Multi-hop offloading can offload data to satellite with sufficient resources by multi-hop transmission, which results in additional transmission energy consumption. Moreover, the dynamic network topology further exacerbates significant energy consumption. Hence, this increased energy consumption may not be sustainable for satellites with limited energy resources. In response, we propose an on-orbit data balancing online algorithm for a LEO satellite cluster, where overloaded satellites directly offload data to idle ones. Designing such a algorithm entails addressing three key questions: determining which LEO satellite to offload, how much data to offload, and how to manage the satellite’s energy storage system. To tackle these questions, we formulate the offloading process as a mixed integer non-linear optimization problem aimed at minimizing overall energy consumption. Subsequently, we devise a repeated stochastic non-cooperative game and leverage an online data balancing algorithm based on Lyapunov to achieve coarse correlated equilibrium for the game. Finally, simulated experiments demonstrate that our proposed algorithm reduces energy consumption by 61.49%, 56.22%, and 55.29% compared to the baselines across three different received data sizes.