On June 18, 1989, Weston picked up his only career major league save. It came against the Oakland Athletics. Weston pitched three shutout innings to close out a 4-2 Orioles victory, saving the game for starter Dave Schmidt. He spent most of the 1990 season with the Rochester Red Wings where he had an 11–1 record with a 1.98 ERA but was .mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}7+2⁄3 innings short of qualifying for the ERA title. He was traded from the Orioles to the Blue Jays for Paul Kilgus on December 14, 1990.
A native of Flint, Michigan, Weston attended Eastern Michigan University. In 1981, he played collegiate summer baseball with the Chatham A's of the Cape Cod Baseball League. He was selected by the Mets in the 12th round of the 1982 MLB Draft.

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