In order to achieve low latency, high throughput, and partition tolerance, modern databases forgo strong transaction isolation for weak isolation guarantees. However, several production databases have been found to suffer from isolation bugs, breaking their data-consistency contract. Black-box testing is a prominent technique for detecting isolation bugs, by checking whether histories of database transactions adhere to a prescribed isolation level. Testing databases on realistic workloads of large size requires isolation testers to be as efficient as possible, a requirement that has initiated a study of the complexity of isolation testing. Although testing strong isolation has been known to be NP-complete, weak isolation levels were recently shown to be testable in polynomial time, which has propelled the scalability of testing tools. However, existing testers have a large polynomial complexity, restricting testing to workloads of only moderate size, which is not typical of large-scale databases. In this work, we develop AWDIT, a highly-efficient and provably optimal tester for weak database isolation. Given a history $H$ of size $n$ and $k$ sessions, AWDIT tests whether H satisfies the most common weak isolation levels of Read Committed (RC), Read Atomic (RA), and Causal Consistency (CC) in time $O(n^{3/2})$, $O(n^{3/2})$, and $O(n \cdot k)$, respectively, improving significantly over the state of the art. Moreover, we prove that AWDIT is essentially optimal, in the sense that there is a conditional lower bound of $n^{3/2}$ for any weak isolation level between RC and CC. Our experiments show that AWDIT is significantly faster than existing, highly optimized testers; e.g., for the $\sim$20% largest histories, AWDIT obtains an average speedup of $245\times$, $193\times$, and $62\times$ for RC, RA, and CC, respectively, over the best baseline.