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Hi Don
One of these 'OE2' weights turned up with an inscription 'For my old friend Jack, June 15, 1851'. There is no reason believe that the date is not genuine, but it not possible to prove it was added in 1851. There was an article about it in PCC Newsletter Issue 96.
In general terms, I think that a good number of Old English paperweights would have been made when these items were fashionable, from 1845 to around 1860. They were made in factories, not by studio artists, and if there was no profit in them they would no longer be made. There is evidence of Richardson making weights around 1900, and of Arculus and Walsh Walsh making them shortly afterwards. My guess is that they would have been made in lesser numbers from 1860 through to 1900, as there were paperweights being made in various places in Europe throughout that period - but as to which English factories, I don't know.
Maybe evidence will turn up to help pin some of these things down - in recent years people have unearthed pages from the 1885 Baccarat catalogue that show the moulded animal weights, and the turn of the century Maltsov catalogue pages that show the Russian plaque and cylinder weights. These provide categoric evidence that the relief moulded bee, lion and dog are not English - and that the intricate plaque and cylinder weights are not Mount Washington.
Alan