Container storage commonly relies on overlay file systems to interpose read-only container images upon backing file systems. While being transparent to and compatible with most existing backing file systems, the overlay file-system approach imposes nontrivial I/O overhead to containerized applications, especially for writes: To write a file originating from a read-only container image, the whole file will be copied to a separate, writable storage layer, resulting in long write latency and inefficient use of container storage. In this paper, we present BAOverlay, a lightweight, block-accessible overlay file system: Equipped with a new block-accessibility attribute, BAOverlay not only exploits the benefit of using an asynchronous copy-on-write mechanism for fast file updates but also enables a new file format for efficient use of container storage space. We have developed a prototype of BAOverlay upon Linux Ext4. Our evaluation with both micro-benchmarks and real-world applications demonstrates the effectiveness of BAOverlay with improved write performance and on-demand container storage usage.