The Rigg-Eng almost certainly refers to England, and was the address of Walter Armstrong who had a son, Walter, on 21/10/171759. The same Walter is also recorded in the Canonbie Old Parish Record as having another son (no name) at Rigdykenook-Eng on 7/12/1761. This is very likely to be the same place.
It was very common for births and baptisms from the Cumberland side of the Border to be recorded in Canonbie, especially those from Riddings and Kirkandrews-on-Esk.
Bealach.