They do represent measurements. I think most companies used those measurements. But for some reason I have been under the impression that one company didn't -- maybe an older company before the measurements were standardized.
This is from an Akro salesman case:
000 is 1/2"
00 is 1/6"
0 is 5/8"
And I just figured out how to remember the rest 1 is 11/16", 2 is 12/16", 4 is 14/16", up to 6 which is 16/16".