Hi Sue, first post on here so hope I'm not barking up the wrong tree but I have an idea as to why you can't find your Jane Fairweather - I'll leave it up to you to prove or disprove either way but this what I'm wondering...
The witnesses at the wedding were, I believe, my gggg grandfather, John Fairweather, 1754 to 1813, and his sister, Elizabeth Fairweather, born in 1751, she would have been 47 at the time of the wedding. The reason for them being there was that their father's father, John Fairweather, 1686 to 1763, married to Elizabeth at St Magdalene, had a son William, 1721 to 1763, who in turn had a daughter Elizabeth Fairweather in 1753. She married Thomas Beecroft in Aug 1773 and they had a daughter Jane. Not surprising that they called her Jane as Elizabeth had two siblings born after her, both called Jane that both died the same year they were born. Anyway, Jane's mother died in 1795 and her father, now a widower, married Anne Pilborough in 1799. I wonder if Jane used her mother's maiden name when she married instead of Beecroft, perhaps because of how she felt about her mother dying and her father re-marrying. Jane was born around 1778 I believe but I don't know what became of her after her mother, Elizabeth Fairweather died and her father re-married. I can't help thinking she could be your Jane that got married in 1798, 3 years after her mother's death. John and Elizabeth would have been witnesses at their cousin's daughter's wedding.
Just an idea, let me know what you think and how you get on.
Kind regards
Gary (my grandmother on my father's side was Lilian Francis Fairweather 1894 to 1972)