Learned indexes fit machine learning (ML) models to the data and use them to make query operations more time and space-efficient. Recent works propose using learned spatial indexes to improve spatial query performance by optimizing the storage layout or internal search structures according to the data distribution. However, only a few learned indexes exploit the query workload distribution to enhance their performance. In addition, building and updating learned spatial indexes are often costly on large datasets due to the inefficiency of (re)training ML models. In this paper, we present WaZI, a learned and workload-aware variant of the Z-index, which jointly optimizes the storage layout and search structures, as a viable solution for the above challenges of spatial indexing. Specifically, we first formulate a cost function to measure the performance of a Z-index on a dataset for a range-query workload. Then, we optimize the Z-index structure by minimizing the cost function through adaptive partitioning and ordering for index construction. Moreover, we design a novel page-skipping mechanism to improve the query performance of WaZI by reducing access to irrelevant data pages. Our extensive experiments show that the WaZI index improves range query time by 40% on average over the baselines while always performing better or comparably to state-of-the-art spatial indexes. Additionally, it also maintains good point query performance. Generally, WaZI provides favorable tradeoffs among query latency, construction time, and index size.