Jay,
Yes that information helps a little. Ballywee is the name of a townland in Kilbride parish. (There is another of the same name nearby in Donegore so be careful when checking records that you have the right one). Ballywee is 298 acres of agricultural land. In the 1860s there were about 40 households in it. In the 1901 census there were 38.
http://www.census.nationalarchives.ie/pages/1901/Antrim/Kilbride/Ballym…
The Kilbride Ballywee is near the village of Doagh. It’s between Hollybank Rd and the Ballymena Rd. There were 2 Brison (Bryson) farms there in the tithe applotment records of 1832. You might expect them to be relations of your John. One held by James and another by Robert Brison. The townland name has “McVicker’s land” attached to it which appears to be an alternative name for the place, at that time.
http://www.irishgenealogyhub.com/antrim/tithe-applotments/kilbride-parish.php#.WVH0txR9eg0
There were no Brysons in the townland by 1862 so evidently the 2 there in 1833 had died or moved.
There are a lot of Presbyterian churches in the area. Kilbride, Ballyclare (with 2), Donegore (with 2) plus a couple in Templepatrick. Not all have records for the 1830s and those that do are not on-line. There are copies of the surviving records in PRONI (the public record office) in Belfast. A personal visit is required to view them.
PRONI also has a lease which could well relate to your John Bryson. It is dated 1st July 1812 and can be found there under ref D509/1811. In the e-catalogue it is described as: “Counterpart lease of 29 acres 2r. 35 per. I.P.M. and of Mill, etc., for 61 years from 1 May 1812 - Rent: £21 2s. p.a. plus fees of Most Hon. George Augustus, Marquess of Donegall to John Bryson, Ballywee, Co. Antrim relating to Ballywee, Co. Antrim.”
This provides the information that John had a farm of just over 29 acres (29 acres, 2 roods and 35 perches to be exact), plus a mill. He leased it from the Marquess of Donegall who was a big landowner in the area. The mill may help identify where the property was.
Looking at Griffiths Valuation there was only 1 mill in Ballywee in 1862. That was on plot 5. So that’s probably the old Bryson property, I would guess. In 1862 the mill was occupied by a John Baird (miller). The mill is shown on Griffiths maps, at the junction of the modern Ballywee Rd and Hollybank Rd. There was a mill pond and other features there, though whether they are still there today, I cannot say. However the location would be easy enough to find.
Being Presbyterian, having a Scottish surname and living in Co Antrim indicates the family originated in Scotland. They probably moved to Co Antrim in the 1600s. Today they are called Ulster-Scots here (Scotch-Irish in North America).