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By the end of 1943, US Navy mathematician/codebreaker Marshall Hall Jr. had developed a system of statistical weights to align JN-25 messages in depth. Although then-current methods of aligning JN-25 messages in depth were working satisfactorily, Hall developed his method "just in case." On 1 December 1943, the Japanese changed the method of numbering the lines and columns of additives on pages of the JN-25 additive book, and Hall's weights, which had been developed "just in case," were needed immediately. This paper discusses both the mathematical idea that was the foundation of Hall's weights and the construction of the weights. It also explores the navy's use of the weights as well as their use at Bletchley Park. At the same time, the navy was exploring the use of two other systems of weights to align JN-25 messages in depth, and those systems of weights are also described. [ABSTRACT FROM AUTHOR]