Adam Rupert was a Loyalist, usually noted as UE for Unity of Empire. Also known as United Empire Loyalist.
DUE and SUE are Daughter of United Empire Loyalist and Son of United Empire Loyalist.
Both DUE and SUE were able to claim 200 acres of land at age 21 or after marriage for girls. These petitions for land are a very rich source of genealogical information since they include proof of filiation as well as other information, such as residence, military service etc.
I recommend you search the UELAC website.
United Empire Loyalist Association of Canada for more precise information about the meaning of UE etc.
Brenda Dougall Merriman wrote a very good blog to explain this on http://brendadougallmerriman.blogspot.ca/2012/02/loyalists-e...