Weiss played just a few tournaments on the ITF Junior Circuit and his only notable junior success was winning Wimbledon doubles crown in '84 partnering Brown. They won the final over Jonas Svensson and Mark Kratzmann despite losing the first set 1–6. As a collegian, Weiss won the 1988 NCAA Division 1 individual singles title despite being ranked only No. 48 in that year's preseason rankings. He did win however three individuals singles tournaments to raise his ranking to No. 1 entering the individual singles championship. In the title match, Weiss defeated UCLA's Brian Garrow 6–2, 4–6, 6–3 to become the first Pepperdine University player win an individual singles title. Weiss was an All-American selection 1986 and again in 1988. In '86 the Waves lost the team championship finals to Stanford.
Turning pro shortly after winning the NCAA individual title, Weiss scored tour singles match wins over at the time World No. 19 Tim Mayotte and No. 31 Karel Nováček both on grass courts in 1990, over World No. 6 Ivan Lendl and No. 21 Henrik Holm on hard courts in 1993, World No. 14 Boris Becker on hard courts in 1994, and most impressively over World No. 2 Stefan Edberg on hard courts in 1992. He won a main draw round at the 1993 Australian Open, over World No. 64 Richey Reneberg, 6–2 in the fifth. In addition to his Grand Prix event triumph in São Paulo in 1990, when he beat Jaime Yzaga in the final despite dropping the first set, Weiss took three Challenger event titles - Itu-São Paulo in November 1992; Palm Springs in 1993; and Granby in 1995.
In doubles, Weiss reached a career-high ranking of World No. 271, in June 1989. He won one Challenger - 1989 Salou, partnering Conny Falk.
United States
Jaime Yzaga
Mark Kaplan
MaliVai Washington
Guillaume Raoux
Roger Smith
Sargis Sargsian
Conny Falk
Mark Kratzmann 