Large language models deployed as multi-step agents are increasingly trained via Direct Preference Optimization (DPO) on trajectory-level comparisons. Yet standard DPO weights every step uniformly, penalizing correct early actions in a losing trajectory as severely as the causal error itself. We propose Divergence-Weighted DPO(dwDPO), a drop-in replacement that detects the first divergence step between competing trajectories using implicit rewards already computed by DPO, then concentrates the loss around it via an asymmetric kernel with a closed-form scale factor that preserves the Bradley-Terry preference model. dwDPO recovers standard DPO as a special case and provably achieves higher gradient concentration at the critical step than both uniform and monotonic-discount baselines. Extensive experimental results across six deep-research benchmarks demonstrate the superiority of dwDPO over state-of-the-art open-source baselines of comparable scale at no additional inference cost.