Schweig was born to an Inuit mother and a Chippewa Dene father in Inuvik, the Northwest Territories. At six months he was adopted by a German-Canadian family. During his childhood in Inuvik, Bermuda and Toronto he was systematically physically abused by his adoptive parents and ran away from home when he was 16, to become a laborer.
In 1987 he was "discovered" while walking down a Toronto street and cast in the movie The Shaman's Source. At least 16 other films have followed, most notably as Uncas in The Last of the Mohicans. During this period he endured a "roller coaster of alcohol, drugs, violence, failed relationships, despair and confusion" [Schweig] due to the abuse and racism and ethnic identity deprivation of his childhood.
In 1996 he began to regain his cultural identity and is now primarily a carver, especially of Inuit spirit masks, living on Vancouver Island, but he continues to act in films. He is a passionate opponent of the adoption of aboriginal of native people by Europeans.