Large language model-based agents operating in long-horizon interactions require memory systems that support temporal consistency, multi-hop reasoning, and evidence-grounded reuse across sessions. Existing approaches largely rely on unstructured retrieval or coarse abstractions, which often lead to temporal conflicts, brittle reasoning, and limited traceability. We propose MemWeaver, a unified memory framework that consolidates long-term agent experiences into three interconnected components: a temporally grounded graph memory for structured relational reasoning, an experience memory that abstracts recurring interaction patterns from repeated observations, and a passage memory that preserves original textual evidence. MemWeaver employs a dual-channel retrieval strategy that jointly retrieves structured knowledge and supporting evidence to construct compact yet information-dense contexts for reasoning. Experiments on the LoCoMo benchmark demonstrate that MemWeaver substantially improves multi-hop and temporal reasoning accuracy while reducing input context length by over 95% compared to long-context baselines.