Regarding the weaving trade, pretty well all agricultural labourers in the Co Antrim area did a bit of weaving, normally in the winter months, when there wasn’t a lot of farm work to be done. The weaving was done at home with portable hand powered looms such as are still used in the Outer Hebrides to make Harris Tweed. They could be dismantled and stored when not required and were portable if the family moved.
Ramoan RC baptism & marriage records only start in 1838 so if that’s the parish where the family lived, there will be no record of any baptisms or marriages before that year. That may be why you are struggling to find anything about them.
The 1803 agricultural census of Ramoan lists 5 Hunter households. Heads of household were: John who lived at Ballycastle Quay, Neal in Drumawillin, Archibald in Drumeeny, John in Kilcreg and Alexander in Townparks (Fort). You can find the census on Bill McAfee’s site: http://billmacafee.com
The 1833 tithe applotment records list 4 Hunter farms in Ramoan parish:
The tithes only listed people with land (ie mainly farmers) so if your family were labourers/weavers they won’t be included. The family in Drumeeny look to have been Church of Ireland (judging by the 1901 census). Can’t say what denomination the others were. Labourers are notorious difficult to trace because they don’t appear in many land records and because they tended to move about a bit to follow the available work. They tended to live below officialdom’s radar a lot of the time, or at least it may seem so.
Ramoan is a different parish to Bushmills. Bushmills is in Ballywillin parish. Their RC records don’t start till 1844 for baptisms and 1848 for marriages.
Outside the big cities, few RC parishes in Ireland have records before about 1825, and so this general lack of baptism and marriage records is fairly common. There aren’t a lot of other records for the early 1800s and so researching the Hunters may prove fairly hard going.