There's quite a lot to respond to here...
William Barraclough:A wool merchant would have been quite wealthy in those days, since it was the basis of much of the booming economy in Yorkshire. There was, incidentally, a firm of weavers in Otley and Bradford called Duncan, Barraclough and Co, but as Barraclough is quite a common name in Yorkshire, there won't necessarily be a connection.
The Ilkley economy:"Pre-Victorian Ilkley 1672-1811" by May F Pickles (Mid-Wharfedale Local History Research Group, 2002; ISBN 0 9533693 1-5) says, "Most farms were relatively small... The pattern of farming was primarily based upon stock rearing and feeding with more farmers keeping cattle than sheep." (p.13)
Later she notes the beginning of a textile industry, though it never developed into anything very significant: the parish registers of 1725 refer to Nicholas Cunliffe (** see below), a worsted weaver, and then "In 1786, William Middleton of Stockeld Park leased land known as Kilner Croft to Thomas Hauxworth of Ilkley, a gentleman [and two others] for the purpose of erecting a stone-built mill..." (p.16)
Urbigan:What caught my eye in the Times law report was the reference to Mr S.C. Lister. This will be Samuel Cunliffe Lister, a massive and controversial figure in the Yorkshire textile industry. There are plenty of references to him online, but this one seems relevant, and mentions the Warburton case:
https://bradfordunconsideredtrifles.wordpress.com/manningham-mill-people/The case has also been mentioned before on RootsChat:
http://www.rootschat.com/forum/index.php?topic=276216.0The Warburton partnership was intended to devise a silk-combing machine, and it appears Warburton baled out before it succeeded. But it may well be that John Hauxworth the younger was in Urbigan in connection with that enterprise. Ideally you'd need to look into whether there were any other Yorkshire companies doing business there at that time.
Anyway, I would recommend that you try to get hold of the actual marriage certificate for John Hauxworth and Ellen Tinker, rather than rely on the version at FamilySearch, since that appears to have confused the residences and places of birth, and it may contain other clues.
As to why the marriage took place there, I'm wondering if it was some kind of elopement because of real or imagined parental disapproval. For example, they could have been of different social class or different religion, or associated with rival companies.
Samuel Cunliffe Lister:I can't really go into him in detail here, but very briefly, he came from the Cunliffe family of Addingham (2 miles upstream of Ilkley, and more or less within spitting distance across the river from Nessfield and Austby), and one family member took the name Lister on marriage.
(** see above) Collyer's book has a Cunliffe pedigree (p.203) which, as well as several Addingham conections, includes a Nicholas Cunliffe 1703-1771. I've skimmed through the Ilkley PRs and can confirm that he seems to be the one mentioned above, but the earliest worsted weaver reference that I noticed was at the burial of a daughter in Sep 1726. He also had a son Henry who married Martha Hawksworth in 1770, but she died the following year. (See also text on p.202 and note at foot of Hawksworth pedigree on p.218.) There's also a mention of the Lister family on p.216.
The Cunliffe Lister family had several mills in and around Bradford, and also developed Low Mill in Addingham. (Warburton was also involved there, apparently.) There are a number of references to the family and their influence on Addingham in "Addingham - A History" by Kate Mason (Addingham Civic Society, 1996).
In view of all this, it seems possible that the Austby Hauxworths might have been distantly related to Samuel Cunliffe Lister. Even if not, I do wonder if at least some of the Hauxworths worked for Lister in some capacity. More research needed, I think, but I'll leave that to you!
Arthur