First - to my knowledge there were never any millefiori paperweights made BY Edinburgh - only FOR Edinburgh: 1986 made by Caithness, later they imported paperweights from Murano.
Now for the weight:
Caithness made a "Miniature Star" in 1986 - different star and only a single ring of millefiori canes.
Caithness also made a "Miniature Bell" in 1986 - exactly the same design as the weight in question here, just with a bell in the centre, not a star.
Neither of the two show up in any publication, but are well documented (and in the queue to be uploaded to ScotlandsGlass).
The canes are typical Caithness canes for the mid-1980ies - no surprise they also show up in the weights made for Edinburgh.
Consequently I'm pretty sure your weight is a mid-1980ies Caithness weight - though one can never be absolutely sure, as there doesn't seem to be any marking to the base (at least you don't mention any). Could well be a trial piece.
Nevertheless - I would appreciate your permission to use your images for ScotlandsGlass, once we have confirmed Caithness as maker.