I looked at my 1950 edition of Part II bought on
ebay and it is housed in a Part II embossed 3 inch binder. While I doubt that this is the original binder (the condition is too good), I don't think the pages would have fit into a smaller binder.
Why is this? I think that even though Part II contains spaces for fewer than half the stamps in Part I, the different categories of stamps within a country (i.e., regular/commems, airmails, postage dues, etc.) are spread out on more pages. Part I also has pages containing more than one country which I don't believe happens in Part II.