Weyrich was born in Racine, Wisconsin, to Virginia M. (née Wickstrom) and Ignatius A. Weyrich. His father was a German immigrant. Weyrich graduated from St. Catherine's High School in 1960 and attended the University of Wisconsin–Madison for two years. He was active in the Racine County Young Republicans from 1961 to 1963 and in Barry Goldwater's 1964 presidential campaign. He spent his early career in journalism as a political reporter for the "Milwaukee Sentinel" newspaper, as political reporter and weekend anchor for WISN-TV (Milwaukee), and in radio as a reporter for WAXO-FM (Kenosha), WLIP-AM, and as news director of KQXI (Denver).