Search agents extend Large Language Models (LLMs) beyond static parametric knowledge by enabling access to up-to-date and long-tail information unavailable during pretraining. While reinforcement learning has been widely adopted for training such agents, existing approaches face key limitations: process supervision often suffers from unstable value estimation, whereas outcome supervision struggles with credit assignment due to sparse, trajectory-level rewards. To bridge this gap, we propose Contribution-Weighted GRPO (CW-GRPO), a framework that integrates process supervision into group relative policy optimization. Instead of directly optimizing process rewards, CW-GRPO employs an LLM judge to assess the retrieval utility and reasoning correctness at each search round, producing per-round contribution weights. These weights are used to rescale outcome-based advantages along the trajectory, enabling fine-grained credit assignment without sacrificing optimization stability. Experiments on multiple knowledge-intensive benchmarks show that CW-GRPO outperforms standard GRPO by 5.0% on Qwen3-8B and 6.3% on Qwen3-1.7B, leading to more effective search behaviors. Additional analysis reveals that successful trajectories exhibit concentrated contributions in specific rounds, providing empirical insight into search agent tasks. Our code is available at https://github.com/zsxmwjz/CW-GRPO.