Angela,
I assume this is your family in the 1901 census:
http://www.census.nationalarchives.ie/pages/1901/Antrim/Court_Ward/Malvern_Street/965571/
If so, it shows that the Craig family was Church of Ireland (ie Anglican).
Belfast in the 1800s went through a major economic boom with over 50 linen mills opening. It was nick-named Linenopolis as a result. The mills employed lots of women (being cheaper and nimbler than men) and as a result hundreds of thousands of women poured into the city, attracted there by the opportunity to get a wage (as opposed to a few coppers for working on a farm or about the house). It was something of a social revolution for women to be able to do this. The new factories were also much more efficient and produced better quality linen than home weaving did, so home weaving (which labourers did in their downtime) was in decline.
https://en.wikipedia.org/wiki/Linenopolis
So that is the likely reason for Isabella’s move from Armagh to Belfast.
The usual reason for marrying in a Register Office was a mixed marriage (ie RC – Protestant). Two Protestants marrying wouldn’t normally go for a Register Office even if of different denominations. Normal practice was to marry in the bride's church after which she’d attend her husbands. There were other reasons for marrying in a Register Office. Folk of a denomination without someone with religious qualifications to perform the ceremony had to use a Register Office. An example would be Brethren (sometimes called Plymouth Brethren). And of course, just as is the case today, there were atheists and agnostics in the 1800s who did not wish to marry in a church. Cost is unlikely to have been a factor. Neither the Church nor the Register Office charged very much. You say you don’t know much about banns. In general, if you are getting married, you have to give public notice (so that folk can object if they know of a valid obstacle). This can be done by reading out the intention to marry 3 times in the couples’ church(es). That’s reading the banns. Or in the case of a Register Office, they post the details on a public notice board outside the office for a specified period before the ceremony. You can also get married by licence, and Presbyterians or folk in a hurry tend to prefer that route. A licence is usually slightly more expensive than banns. If Thomas and Isabella were both from Protestant backgrounds, then it’s possible that neither was a church goer. That might be the explanation for marrying in a Register Office.
To trace Isabella’s birth, ideally you would need to know her precise denomination at birth and which parish she lived in. Not all the records from c 1835 have survived and of those that do exist, not all are on-line. The most complete collection is in PRONI in Belfast but there would be quite a lot of records to go through, for Co Armagh if you don’t know where she lived. It could be done though. Researchers in the PRONI area: http://sgni.net
Photo and article about Ewart’s Mill here:
https://www.belfasttelegraph.co.uk/news/northern-ireland/fears-over-pro…