PRONI has a record of John Tweed of Mullans voting on 30.5.1776. Ref D 1363/L/1. It was to elect the 2 MPs for Co. Antrim for the Irish parliament in Dublin, and voting was in Carrickfergus. That he could vote indicates John was a farmer or landowner with land of £2 a year or more rental value, or something similar. Quite well off by the standards of the time. (The vast majority of the population weren’t eligible to vote because they did not meet the land value threshold).
I cannot find any other reference to the Tweed family in Mullans. They weren’t listed in the 1834 tithes nor Griffiths Valuation. All had apparently left by then.
None of the Finvoy parish church records go back to the 1700s. The Church of Ireland records start in 1811 and the Presbyterian records in 1843. (I’d guess from his surname, and also the period that he left Ireland, that your ancestor was Presbyterian and therefore of Scottish origins).
You could search the Registry of Deeds records to see of there are any Tweeds in Mullans. (Search under townland not by surname). Those records start in 1708 and are in PRONI and also on the LDS site. That might throw up a lease or other deed for the family for the 1700s. Otherwise I think you wills struggle to find any record of them in Ireland.
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project in conjunction with Family Tree DNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website). You don’t need to be a member of the NIFHS to participate in the DNA project.
