Since my previous post, I found a second possibility. I am posting images of the records (Saas) here in case you wish to review them.
One is a Kilias Weber, Line 158, born 15 Nov 1848; parents Bartholome Weber son of Peter Weber and Barbara Marugg, and Margaretha Mathis daughter of Kilias Mathis and Anna Werli.
Second is Kilias Weber, Line 183; born 18 Nov 1850; parents Peter Weber son of Peter Weber and Barbara Marugg, and Christina Mathis daughter of Kilias Mathis and Anna Werli. (i.e. the grandparents were the same). If you are still looking for Killian, I hope this helps a bit. Perhaps Kilias was the German spelling of Killian...good luck!!