Clinical text improvement is vital for healthcare efficiency but remains difficult due to limited high-quality data and the complex constraints of medical documentation. While Large Language Models (LLMs) show promise, current approaches struggle in small-sample settings: supervised fine-tuning is data-intensive and costly, while retrieval-augmented generation often provides superficial corrections without capturing the reasoning behind revisions. To address these limitations, we propose ExperienceWeaver, a hierarchical framework that shifts the focus from data retrieval to experience learning. Instead of simply recalling past examples, ExperienceWeaver distills noisy, multi-dimensional feedback into structured, actionable knowledge. Specifically, error-specific Tips and high-level Strategies. By injecting this distilled experience into an agentic pipeline, the model learns "how to revise" rather than just "what to revise". Extensive evaluations across four clinical datasets demonstrate that ExperienceWeaver consistently improves performance, surpassing state-of-the-art models such as Gemini-3 Pro in small-sample settings.