Maymie,
A few comments.
Nancy & Agnes are interchangeable names in Ireland and Scotland so it’s common to see both in reference to the same person.
You mention that the McKee family were Presbyterian. However St Anne’s where David was baptised in 1809 is Church of Ireland (ie Anglican/Episcopalian). So are you sure you have the right David McKee baptism? Are his parents names on his death certificate for example?
I searched the 1807 & 1808 street directories for Belfast for a Hamilton McKee but did not find one, but not everyone was listed:
https://www.lennonwylie.co.uk/1807.htm
The agricultural census in 1803 was by its nature a rural survey. People living in towns and cities such as Belfast weren’t included, since they weren’t engaged in agriculture. So if the Belfast Hamilton was living there in 1803, he wouldn’t be included. But he might have moved to Belfast between 1803 and 1808. There’s no easy way to tell. Hamilton McKee is a relatively unusual name, and even if it’s not the same man, there might be a family connection. However I did find evidence that there was more than 1 person named Hamilton McKee. See this link to the Ros Davies site which gives 4 references dating to the 1860s & 1870s:
http://freepages.rootsweb.com/~rosdavies/genealogy/SURNAMES/Mc/McKeeAi…
The 1834 tithe applotment records list a Gown McKee and a John McKee both farming in Drumnascamph. Possibly a connection to the 1803 family:
http://www.irishgenealogyhub.com/down/tithe-applotment-books/clonduff-parish.php
Griffiths Valuation for 1864 lists 4 McKee properties in Drumnascamph (which is about 50 miles south of Belfast): 2 John McKees, David McKee and Gawn McKee. John McKee (Bridge) had plot 5 which was a 23 acre farm; John McKee (fat) had plot 15 a 24 acre farm; David Mckee had plot 16 a 17 acre farm and Gawn McKee had plot 17 a 4 acre farm.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
So there does not appear to have been a Hamilton McKee there by 1864. And there were no McKees there by the 1901 census:
http://www.census.nationalarchives.ie/pages/1901/Down/Tullyish/Drumnascamp/
Regarding finding marriages, tradition was to marry in the bride’s church, after which she’d usually attend her husband’s. So the marriage can often be in a different church to the one in which the couple’s children were later baptised.
Secondly, not all churches have records for the early 1800s, and of those that do, they are not all on-line. (St Anne’s is on-line but many other churches – and there are about 200 altogether in Belfast – are not on-line). The most complete collection of church records for the counties of Ulster is in PRONI (the public record office) in Belfast. A personal visit is required to view them though. If you think the Drumnascamph familiy might be yours, Clonduff Church of Ireland has records from 1782 onwards. There are 2 Presbyterian churches in the parish. Clonduff Presbyterian has baptisms from 1842 onwards and Hilltown from 1845 onwards. (Copies of all those records are in PRONI).
Don’t expect too much from early Irish records. In the early 1800s most marriages simply recorded the couples names, the date and their 2 witnesses. Nothing more. Likewise baptisms often only contain the parents names and the date (sometimes only 1 parents name). Occasionally you get a townland but in Belfast there was rarely an address or occupation.
I can see that the 1841 census has a James McKee aged 25 and born Ireland living with David & his family in Bridgeton, Glasgow. Like them he was a cotton hand loom weaver. Have you researched what happened to him? Presumably he was a close relative – David’s brother perhaps? (Incidentally in the 1841 census (only) adults ages were rounded down to the nearest 5 years. So James could be anything between 25 & 29. Children up to 15 were recorded with their actual ages).
There’s a death on 4th July 1868 in Bridgeton for James McKee aged 47, son of Hamilton McKee & Margaret Baird. So, if his age at death is accurate (and it may not be) he was born c 1821. He was a cotton loom weaver and married to Elizabeth Moore. (They married in Bridgeton in 1866). Hamilton McKee was also a cotton weaver but was dead by 1868. Margaret Baird was still alive. The informant was James' brother John McKee.
I can see some trees on Ancestry (the Moss family for example) which have “your” Hamilton McKee dying in Scrabo Co Down on 23.8.1861. (There is a will on the PRONI website for that man). However that Hamilton was a farmer who left his farm to his son Hamilton. According to his will, the Scrabo Hamilton’s wife was named Mary Johnston alias McKee. Different occupation and different wife mean it’s not the same Hamilton as the one married to Margaret Baird. So that would appear to be inaccurate information on those trees. A common problem. Some of the trees list another child to Hamilton & Margaret. John born Scotland 1826 and died in Glasgow 1892. I can’t say how accurate that is but you might want to investigate it.
I notice a Hamilton McKee baptised in Glasgow (St Mary’s parish) on 15.11.1852 to John McKee & Mary Boyle. A catholic ceremony. That child appears to have died in Bridgeton in 1863 aged 10.
I had a look for Margaret McKee deaths 1868 – 1900 in Ireland. There were 352, of which there were 50 in Belfast. You could plod through them all - they are mostly free to view on the irishgenealogy site - and see if you can spot Hamilton’s widow. You are obviously looking for someone born 1790 or earlier, probably in one of the Ulster counties, so it should be possible to eliminate many of the 352 fairly quickly. (I looked for her death in Scotland which is easier to do, but didn’t see it there).
A little general information about Belfast in the 1800s. The population of Belfast expanded dramatically in the 1800s. In it’s early years it was largely Presbyterian (being dominated by Scots who had moved to Ireland in the 1600s). The population of Belfast in 1800 was about 20,000. In 1901 it was 349,000. The establishment of the shipyards, 50 linen mills and countless support industries led to a huge influx of workers from the surrounding countryside who were looking for better paid jobs in the city.
Your ancestor might have been born in Belfast but it’s equally possible that he or his parents were amongst the tens of thousands who were pouring into the city every year around that time.
A little information about weaving. In rural areas most weaving was done at home using hand loom weaving machines, such as are still used in the Outer Hebrides in Scotland to make Harris Tweed. These machines were collapsible, so as to be stored out of the way when not needed and for ease of transport should the weaver move home, as they often did, to follow the available work.
Most weavers in Ulster were labourers who earned a bit of extra money by weaving in the winter months when there wasn’t much labouring work required on farms. This meant that labourers in Ulster had a slightly better standard of living than elsewhere in Ireland. It also gave them some ready cash (in a society that mostly operated by barter) for the things that could not be bought by barter, eg a ticket to America or Canada.
At one time weavers wove a lot of cotton but the interruption of supplies from the southern US states during the American War of Independence in the 1770s meant they focused on other materials, notably flax (which linen is made from) and which grows well in Ireland in contrast to cotton which won’t grow at all. They did weave other products eg calico and wool as required, but by the 1800s it was mainly linen. Linen made at home was taken to the local linen market and sold there.
As the 19th century progressed, water powered linen mills were introduced all over Ulster. These were faster than home weavers and often made better quality material and so gradually made the home weaver redundant. In addition, the factories also mostly employed women and children (being nimbler and cheaper) so this impacted on male employment too. At a time when farms were starting mechanise and so needed fewer labourers, the average labourer/weaver therefore faced a bleak future and so these combined changes were a major factor in many a labourer’s decision to leave Ireland during the 1800s. A little more information on this link: https://www.irish-genealogy-toolkit.com/flax-plant.html