Weiss played just a few tournaments on theITF Junior Circuit and his only notable junior success was winning Wimbledon doubles crown in '84 partnering Brown. They won the final overJonas Svensson andMark 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 defeatedUCLA'sBrian Garrow 6–2, 4–6, 6–3 to become the firstPepperdine 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. 19Tim Mayotte and No. 31Karel Nováček both on grass courts in 1990, over World No. 6Ivan Lendl and No. 21Henrik Holm on hard courts in 1993, World No. 14Boris Becker on hard courts in 1994, and most impressively over World No. 2Stefan Edberg on hard courts in 1992. He won a main draw round at the1993 Australian Open, over World No. 64Richey Reneberg, 6–2 in the fifth. In addition to his Grand Prix event triumph in São Paulo in 1990, when he beatJaime Yzaga in the final despite dropping the first set, Weiss took threeChallenger event titles - Itu-São Paulo in November 1992; Palm Springs in 1993; andGranby in 1995.
In doubles, Weiss reached a career-high ranking of World No. 271, in June 1989. He won one Challenger - 1989 Salou, partneringConny Falk.
United States
Jaime Yzaga
Mark Kaplan
MaliVai Washington
Guillaume Raoux
Roger Smith
Sargis Sargsian
Conny Falk
Mark Kratzmann