A "background statement" first: to my knowledge, Edinburgh Crystal never produced any millefiori paperweights. In the mid-1980ies they commissioned some from Caithness (see
here) and afterwards from Murano (not sure which maker or makers).
There is a
thread on this topic about a weight looking similar - with a silver label "Edinburgh - International - Handmade - Italy" ... unfortunately the image is gone: if the moderators want it (to add it to the thread again) - let me know - I have copied it.
There also have been several on auction over the years (mostly ebay) - looking similar, with labels "Edinburgh - International - hand cut - imported", some sold in cylindrical cardboard boxes with "Edinburgh International" imprinted.
Conclusion: Murano weights have been sold by Edinburgh Crystal, but always (at least originally) marked as imported or Italian.