"To systematize a plan for my work I arranged the papers in the order of their length, and numbered them, designing to commence with the first, and devote my whole attention to that until I had either unravelled its meaning or was convinced of its impossibility--afterwards to take up the others and proceed as before.
All of this I did in the course of time, but failed so completely that my hopes of solving the mystery were well nigh abandoned. My thoughts, however were constantly upon it, and the figures contained in each paper, in their regular order, were fixed in my memory."
Notice both times he used the word "order." 1st he said order OF THEIR LENGTH, so what would he have meant by the 2nd use of the word "order"? It's the way the papers were originally ordered, as opposed to the order by length. Numbering them by length failed, so he went back to the way they were originally ordered. When he arranged them according to their length, he NUMBERED them that way, therefore, when he went back to the original order, he went back to the way they were originally numbered. The other way failed.
"The letter, or paper, so often alluded to, and marked "2," which is fully explained by the foregoing document, is as follows..."
"It would be difficult to portray the delight he experienced when accident revealed to him the explanation of the paper marked "2.""
Why would that certain paper be marked #2? It would not be marked #2 by length.
Decoded paper#2: ...articles, belonging jointly to the parties whose names are given in number "3," herewith:.
...The vault is roughly lined with stone, and the vessels rest on solid stone, and are covered with others. Paper number "1" describes the exact locality of the vault, so that no difficulty will be had in finding it....
Why are these numbers in quotation? Remember, this is not the author, but rather Beale himself that gave these numbers, and they are in quotation. If the papers had not been numbered, then it would not make sense to allude to them by their numbers, especially when the numbers are in quotation.