In video search systems, user historical behaviors provide rich context for identifying search intent and resolving ambiguity. However, traditional methods utilizing implicit history features often suffer from signal dilution and delayed feedback. To address these challenges, we propose WeWrite, a novel Personalized Demand-aware Query Rewriting framework. Specifically, WeWrite tackles three key challenges: (1) When to Write: An automated posterior-based mining strategy extracts high-quality samples from user logs, identifying scenarios where personalization is strictly necessary; (2) How to Write: A hybrid training paradigm combines Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO) to align the LLM's output style with the retrieval system; (3) Deployment: A parallel "Fake Recall" architecture ensures low latency. Online A/B testing on a large-scale video platform demonstrates that WeWrite improves the Click-Through Video Volume (VV$>$10s) by 1.07% and reduces the Query Reformulation Rate by 2.97%.

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