I have a locally written booklet about Upperby Church and the history of Upperby and there is a small passage in it where Alexander Robinson receives a brief mention.
It reads "With peaceful times that followed the failure of '45 Upperby became more prosperous. Hand looms were erected in many of its houses which earned over £1 per week. By 1829 Upperby's main industry was damask weaving carried on by Isaac Fell and Alexander Robinson,"
It sound as if Alexander (b 1777) may possibly have been the 3rd generation of damask weavers in Upperby. There is a death notice possibly for his father (Alexander b 1744) in Carlisle Journal 9 March 1805. The above passage implies that his grandfather may have started the weaving after the Bonnie Prince Charlie uprising of 1745.
There is also a details of the number of families that lived in Upperby in 1780: 20 houses, 21 families, 35 males, 54 females, so at that point in time its looks like most of the weaving was taking place in the home, a lot which were clay daubins.
(not sure where you are, but if you need someone to look up what the Cumberland News article is about or the 1805 Will I could do that)