The definition of "mangnum" differs between makers or companies. It probably also differs between authors, too.
My understanding is that 3.5 inch (9 cm) diameter is the smallest size that really can be called "magnum". As with the Murano size of 3.25 inch (8.3 cm), a lot of Paul Ysart weights were that 'standard' size, too.
The first edition (but not the second, it seems!) of, The Charlton Standard Catalogue of Caithness Paperweights
defined magnum as 110mm [that's 4 5/16 inch according to my slide rule]. Their standard size was stated as 80mm [3 1/8 inch].
Paul Dunlop, in his book, The Dictionary of Glass Paperweights an illustrated primer
, 2009, says:
Any paperweight from the classic period which is 3 1/4 inches ...
["Classic period" = 1845 - 1870 (ish)] He goes on to say that because 3 1/4 inches is a standard size for many of today's makers, then magnums should be "larger than 3 3/4 or 4 inches". Hmm, I wonder why he did not include 3.5 inch (9cm) in the definition?