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I think you have asked a very important question, Nicholas. I am trying to answer it in my article as far as I can, but to my knowledge there is no documented link to any Old English paperweights from the mid 19th Century that proves who made which ones. No documented link whatsoever between 'classic Bacchus weights' and the maker George Bacchus (though I do think it there is a reasonable case for linking the two). I take the view that the very few 'IGW' weights can be attributed to Islington with reasonable confidence (as manufacturer of the weights, rather than maker of all the canes), but beyond that, it is - as you suggest - mainly folklore for items from the 1850 - 1900 period. And some of that folklore was defined in the mid 20th Century or later.
There is solid evidence to confirm the Arculus pieces with the fake '1848' dates from the 1920s-1930s, and the subsequent Walsh Walsh paperweights. Also for Richardson 'footed' weights and bottles from the 1900 - 1914 period. There is evidence too for the existence of a few Whitefriars paperweights from the late 1930s (but definitely not before then). What we cannot determine is which (of many) factories made the high quality OE paperweights in the 1845 - 1860 period. There are plenty of candidates: high quality glass makers who exhibited and won medals at major exhibitions, but no hard evidence has been found to date, as far as I know. The Richardson family left glass to Broadfield House museum, but no paperweights...
So what about Gammon & Sons, Joseph Green, Lloyd and Summerfield, James Stevens, Samuel Shakespeare, Walsh Walsh, and more...all high quality glassmakers in Birmingham around 1850? Any or all of them may have made paperweights. And there were more candidates a few miles away in Stourbridge, including Richardson, Webb...
Alan