We study weighted paging with delay, a generalization of classic paging that permits serving requests after their arrival at the cost of incurred delay. This model enables batching of requests but introduces substantial difficulty due to overlapping intervals. In the unweighted case optimal $O(\log k)$‑competitive algorithms are known, while the best prior randomized algorithm for the weighted case (Gupta, Kumar, and Panigrahi) achieves $O(\log k \log n)$ competitiveness, leaving a gap. We present a randomized $O(\log k)$‑competitive algorithm, matching the lower bound from classic paging. The main idea is a structural decomposition that separates the evolution of the cache over time from the scheduling of extra page loads, ensuring feasibility. We first apply this to paging with time windows, where each request must be served within a prescribed interval. Given a sequence of cache configurations, we reduce the augmentation problem to a variant of the Joint Replenishment Problem with deadlines (JRP‑D) that has time‑dependent opening costs. For this variant we design a constant‑competitive online algorithm under a prediction model whose information is available online in our paging reduction. Combining this with an existing online construction of cache configurations yields an $O(\log k)$‑competitive algorithm for paging with time windows. We then extend the framework to weighted paging with a general delay function, preserving the same guarantee.\n\nReview