What about the Ireland side?
Earliest records I can find is some marriage and baptism stuff at Saint Bridget's in Drumcong, Leitrim.
The Catholic Parish has existed in various forms as Saint Bridget since roughly 1400 and before that was called Saint Patrick.
The current building is modern and the graveyard is from 1800s.
There are still McWeeneys there but no idea who they are as my last grand father born there was 1860 and he died in New Haven, CT in 1914.