[3] He is brother to Professor Lydia Wevers (Director of the Stout Research Centre at Victoria University).

Wevers was educated at Rathkeale College from 1965 to 1969,[4] and went on to Victoria University of Wellington, graduating with a BSc and BA (Hons) in economics.

He joined the Ministry of Foreign Affairs, European Division, in 1977 and in 1982 was Second Secretary at the New Zealand Embassy in Japan.

Between 1989 and 1992, Wevers served as Counsellor in the New Zealand Embassy, Brussels before becoming High Commissioner to Papua New Guinea (1993–1994) and as Ambassador to Japan (1994–1997).

In the 2012 Queen's Birthday and Diamond Jubilee Honours, he was appointed a Knight Companion of the New Zealand Order of Merit (KNZM) the first CE of the Department of Prime Minister and Cabinet to have been recognised in this way.