Large Language Models (LLMs) have fundamentally transformed natural language processing (NLP), demonstrating remarkable capabilities across a wide spectrum of tasks. However, when applied to instruction-based text editing, LLMs continue to exhibit some limitations. Different from free-form generation, instruction-based editing requires precise, targeted modifications that respect two essential properties: faithfully implementing the specific instruction and local fidelity. Existing approaches often overlook these properties, treating editing as a generic text generation problem. As a result, they either over-edit or fail to apply modifications consistently. To address this gap, we propose HyperEdit, a framework that adaptively processes each editing request to best align with it. To achieve this, HyperEdit generates request-specific dynamic weights that guide the editing process. The computational overhead of producing these weights is minimized through a carefully designed hypernetwork. With this design, HyperEdit achieves a relatively 9% improvement over the state-of-the-art editing model.