Web agents must choose queries, clicks, form fills, and tool calls from language instructions while preserving constraints whose consequences may appear several steps later. We study this challenge as language-conditioned delayed-constraint tracking and present TraceWeaver, which couples linear-time latent rollouts, entity-centric episodic memory, and a learned critic for budgeted action selection. Across WebShop (500 episodes), Mind2Web (1,000-task split), WebArena (812-task split), and WorkArena (165-task enterprise split), TraceWeaver shows task-success gains of +2.7 to +4.7 over baselines under a matched test-time budget. Shared-pool controls reduce the confound between selection quality and proposal quality, while a language-phenomenon analysis concentrates the gains on tasks with dense, conflicting, or delayed constraints.

Long-horizon language agents must decide not only which evidence to use, but also when to pay for it. Retrieval and verification can improve a local decision while exhausting token and tool-time budgets needed later in the episode. We introduce ReserveGate, a one-step evidence controller that combines an explicit uncertainty sketch, an off-policy action-value model, and component-wise feasibility masks over the remaining resources. Unlike a fixed reserve heuristic, ReserveGate adapts its cost penalty when spending runs ahead of episode progress and gradually releases a protected late-stage reserve. Across three benchmark-derived agent environments, ReserveGate improves tight-budget success over the strongest matched controller by 2.6–3.8 percentage points, with gains of 4.6–6.2 points on the longest episode quartile. A latency-constrained variant reduces service-level incidents to 1.2–1.7% across environments while losing at most 0.8 points in success. On LoCoMo-Episodic, cross-model, cross-retriever, rate-limiter, and task-agnostic-sketch comparisons show that the effect is not explained by a single backbone, retrieval stack, or tuned spending rule.