GUI agents are beginning to operate the web, mobile, and desktop as interactive worlds, where successful control depends on carrying forward visual, procedural, and task-level evidence beyond the fleeting present screen. Yet most agents still treat memory as an external, human-readable artifact: histories are summarized, categorized, retrieved, and reinserted as text or structured records before being encoded again by the policy. This creates a mismatch between the representational form in which experience is stored and the latent embedding sequence over which modern GUI policies actually act. We introduce Mem-W, a series of latent-memory-native GUI agents that treat memory as part of the agent's continuous context rather than as an auxiliary symbolic scaffold. Mem-W weaves both historical trajectories (as experiential memory) and in-session segments (as working memory) into compact memory tokens through a shared trajectory-to-latent compressor. These tokens are woven with the current GUI observation and local context into one continuous embedding sequence, allowing the agent to read successes, failures, and unfinished progress through the same machine-native interface. Mem-W is trained with self-distillation and outcome-aware supervision to preserve decision-relevant state while filtering memory toward evidence that truly supports task success. Across four web and mobile navigation benchmarks, Mem-W consistently improves diverse backbones and memory-enhanced baselines, with gains of up to $+30.0$, suggesting that latent-context-native memory can serve as a scalable foundation for long-horizon GUI agency.