In his first year of life, his family left for Curaçao. In 1955, he returned to the Netherlands by boat. He studied Architecture at Delft University of Technology. In 1966, shortly after finishing his studies, he won the Prix de Rome for Architecture with a plan for a new Central Station in Amsterdam. One of his first works in 1969 was a vacation home in Veere for a family member. From 1970 to 2003, he was a professor at the Faculty of Architecture at TU Delft. At the same time he worked as an architect. For some time he worked under his own name. For the Dutch pavilion of the 1970 World Exhibition in Osaka, he collaborated with J.B. Bakema of the architectural firm Van den Broek and Bakema. Of slightly later date is the Blijenhoek housing plan on the edge of Dordrecht's downtown. In 1977 he associated himself with the Architectenbureau of Jan Hoogstad c.s. In 1988 he left this bureau and founded the Architecten Cie. with Jan Dirk Peereboom Voller, Pi de Bruijn and Frits van Dongen. Weeber is known as a fierce opponent of the so-called New Truttiness in Dutch architecture. That was the small-scale housing construction of the late 1970s, with its housing estates. As a counter-reaction, he designed some colossal buildings. He designed a hospital for North Vietnam in the late 1970s that was prefabricated entirely in the Netherlands, shipped to North Vietnam and assembled there. Two more hospitals later followed in Guinea-Bissau and Tanzania. From 1993 to 1998, he was president of the Association of Dutch Architects (BNA). In a survey by the Volkskrant (1997), he was proclaimed the "worst architect" in the Netherlands by fellow architects. In 1997 he launched the concept of "Het Wilde Wonen" as a protest against rigid Dutch housing construction, in an interview with Bernhard Hulsman, editor of NRC Handelsblad (Cultureel Supplement of April 4, 1997). A tamed variant of "Het Wilde Wonen" became the "Gewild Wonen." As of 2003, he called himself ex-architect. 50 years after coming to the Netherlands, he returned to Curaçao in 2005, where he had designed a house for himself. Weeber is Knight of the Order of the Dutch Lion. In 2006, he received the Rotterdam-Maaskant Prize.