As Roger said, the surname Ruane is mostly a Mayo name, although it may have originated a bit further south in what is now Galway. One of my grandmothers grew up in Killasser parish in Mayo, which borders Sligo, and she had a number of Ruane relatives living in that parish. The parish records for Killasser only go back to 1847, so they would not be of much use, but the neighboring parish of Swineford/Swinford (also called Kilconduff or Meelick) has some records available online for the 1820's, and I've found some relatives there, presumaby baptIzed or married there at a time whe there was not yet a church building in Killasser. Those records are available at this link:
https://registers.nli.ie/parishes/0133
I checked Griffith;s Valuation, which was a mid-1800's tax census, and there were 32 Patrick Ruane's listed as tenants or landowners in Mayo, almost all of them within a few parishes northwest or southeast of Killasser (though none actually in Killasser itself). You can see the list here:
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNam…
If Mary was from Mayo and her father was alive at thhe time of Griffith's Valuation (and held a tenancy), then he's likely to be one of those 32.
MacLysaght, in his Surnames of Ireland, says that Ruane is an anglicization of the Irish surname Ó Ruadháin, which is based on the word ruadh. meaning "red" or "red haired" (so "descendant of the red-haired one"). It has also been anglicized as Rowaine, Raine, Rouine, Royan, and even Ryan in some cases (most Ryan's being of a different origin)..
For McWeeny, he says that it is an anglicization of the Irish surnme Mac Mhaonaigh (which has an ambiguous meaning), and originated in what is now Roscommon, though (as Roger said) it is now more common in Leitrim. I did a search in Griffith's Valuation, to see whether there might be any McWeeny's or McQueeny's in Mayo or nearby parts of Roscommon, and there were none shown. That may mean that the couple only met once in England. After the Famine, many people in East Mayo went seasonally to England, Scotland, or Wales for work (and some stayed there, of course), and I assume that was true for people inn Roscommon and Leitrim as well, so they may have met that way.
