Composed Video Retrieval (CVR) aims to retrieve a target video given a reference video and a modification text. The central challenge is to identify and use video content that is relevant to the retrieval need specified by the modification text. Existing methods typically encode videos before considering this textual need, causing visual evidence to be formed in a largely text-agnostic manner. We propose StaDy-CLIP, a compact dual-pathway framework for text-conditioned evidence composition. It preserves the frozen CLIP visual encoder as a static pathway for CLIP-aligned static evidence, introduces a lightweight side pathway for dynamic evidence, and uses Text-Conditioned Composition Blocks to perform patch-wise dynamic evidence selection and textual modulation. A learnable Gallery Conditioning Prompt further enables gallery videos to be encoded within the same evidence composition framework. StaDy-CLIP achieves state-of-the-art performance on FineCVR-1M and TF-CoVR with only 7.78M trainable parameters, improving prior best results by +4.05 in Recall@1 and +1.49 in mAP@5. Ablations and encoder-transfer results validate its effectiveness and encoder-level transferability for existing CVR methods.