The title to your post puts William & Mary in Cortown, Co Meath. The post itself is under Co Antrim. However when I search for a marriage for this couple I find what looks like them both living in Co Down in 1855. So some confusion there. I’d be surprised if someone marrying in Co Down originated in Meath, though it’s possible. What’s the source of that birth information? (Hopefully it’s not just an Ancestry hint is it? If so, best disregarded). There is a townland called Cotton near Newtownards. I wonder if there’s been some confusion between it and Cortown in Meath? William’s occupation was a miner and his address was Ballygowan, parish of Comber. Father Alexander Steele, labourer. Mary was living in John St, Newtownards and her father Robert was another labourer. Ballygowan and Newtownards are both close to each other in Co. Down.
Tradition was to marry in the bride’s church which was Newtownards Church of Ireland (ie Episcopalian) so that's possibly where you might expect to find a record of Mary’s baptism and that of any siblings. Unfortunately that church’s records were destroyed in the 1922 fire in Dublin and they have no baptisms earlier than 1884 and no marriages before 1845. A Samuel Steele was a witness, so he’s presumably a close relation.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1855/09497/5441862.pdf
That William’s 1855 occupation was a miner suggests he was already working in Scotland. There are no mines anywhere near Ballygowan (and very few mines in Ireland generally) so he had probably just come home to marry.
If William & Mary both died in Scotland, it should be possible to get their mothers’ names from the Scottish death certificates which would aid searching for their deaths in Ireland.
Here’s a possible death for an Alexander Steele in Newtownards workhouse:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1884/06329/4815198.pdf
And another in Ballygowan:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1883/06379/4831170.pdf
I can see from Ancestry that there are trees that say William’s mother was Margaret McMeachan. (That’s likely to be McMeekin or McMeechan in Ireland. It’s a common Scottish name around Ballygowan). Here’s a death in 1875 in Ballygowan that probably fits. Informant Alexander Steele.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1875/020638/7240982.pdf
Griffiths Valuation of 1863 lists Robert Elliott in John St, Newtownards. He had a house, yard & small garden. This looks to be his death in 1876. Informant was Susan Elliott.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
You are obviously curious as to why William & Mary went to Scotland. Ireland lacks natural resources. No coal, oil, iron ore etc, and so apart from a modest amount of shipbuilding in Belfast and the Belfast linen mills, it did not really get the industrial revolution that benefited England and Scotland where mills, steelworks, ship building, coal mining and all their support industries were major employers creating hundreds of thousands of new jobs. Much better paid than subsistence farming or hand loom weaving. Agricultural mechanisation was also slowly reducing the need for farm labourers. (Labourers usually did weaving in the winter months when there wasn’t much farm work needed).
Added to that you had the effects of a massive population explosion in Ireland – up from 3 million in 1750 to 8 million in 1841 (no-one is really sure of the reasons why but reduced neo-natal deaths seem to be a factor) and the famine. So some push factors and some pull factors saw huge numbers of people leave Ireland. Something like 8 million people emigrated from Ireland between 1801 & 1921.
https://www.irish-genealogy-toolkit.com/emigration-Ireland-19th-century.html
If you look at the Scottish censuses for the Glasgow area in the late 1800s, you will see that about every fifth person recorded there was born in Ireland. Scotland was a particularly popular place to go to work because it was easy and very cheap to get to. Several sailings every day from Belfast, plus regular sailings from Portrush, Ballycastle and Londonderry, not to mention Dublin. The shipping companies main business was cargo and the passengers were just top-up revenue. Competition was fierce and passenger fares very low. People working in Scotland could come home for weddings or the harvest, as well as holidays (Glasgow used to shut down for 2 weeks every July, known as the Glasgow Fair holiday and there would then be a huge exodus to Ireland). You could also send children back to stay with their grandparents, thereby leaving the wife free to work. You couldn’t do all those things so easily from Australia, America or Canada.
You ask about the weaving industry. Throughout the 19th century home weaving became uneconomic as it was replaced by water powered mills which turned out generally higher quality cloth, much more quickly and more cheaply. The mills tended to employ mostly women or teenagers (being cheaper and nimbler than men) and so that impacted on the average farm labourer/weaver too. The US civil war didn't impact the Irish weaving industry very much as it was mostly making linen, which comes from the flax plant which is grown locally in Ireland. So the lack of cotton imports in the 1860s didn’t have that much of an impact. (The US war of independence c 1776 did have a major impact in Ireland and saw the switch from cotton to linen and other forms of weaving eg wool, but that was 80 years earlier).
The main financial driver for the move to Scotland was simply the availability of much better paid jobs. Same thing that drew thousands from the Scottish highlands and lowlands for those jobs too. I wouldn't see it as exploitation of the Irish, or even the Scots (who got the same wages), just economic betterment.
As far as DNA is concerned, the Steele, Elliott & McMeechan families are likely to be descendants of Scots who moved to Co Down in the 1600s, as part of a major Scots migration there throughout that century. (Half the county has the same roots). So ultimately, your “Irish” DNA should take you back to Scotland. Those ethnicity tests are not very accurate. More of a guesstimate, so I wouldn’t rely to heavily on them for accuracy.