Onboard supercapacitors (SCs) charging usually requires fast charging with high current. In the constant current charging mode, a distributed multi-module charging system model is established to decompose the ultra high power from fast charging process. However, current overshoot and current imbalance in fast charging mode are prone to damage the reliability of charging system. In this paper, a Weight-optimizing Cooperative Charging Algorithm (WCCA) for onboard SCs is proposed to solve these problems. The key idea of WCCA is to design the dynamic correction weight factors to optimize the performance of current overshoot, imbalance and charging speed in three stages. Then, we prove the stability of the proposed algorithm through Lyapunov stability theorem. The impacts of current overshoot and imbalance on the charging system are evaluated through deviation distribution under noise mathematically. Compared with the existing cooperative charging strategies, WCCA scheme suppresses current imbalance and decreases current overshoot noticeably, while catching up with desired current quickly. Simulation and experiment results are provided to illustrate the feasibility and effectiveness of the algorithm.