Joseph Leonard Weber, who from 1757 was a burgher of Buda, was probably born in Silesia into the Weber dynasty of sculptors in Schweidnitz. The family originated from Frankish territories, its first known sculptor is Johann Balthasar. His son, Georg Leonhard Weber (around 1670-75 - after 1732) already lived in Schweidnitz, and here were baptized his five sons, among whom there become sculptors.

Joseph Leonard Weber, born in 1702, may have come from this generation of sculptors to southern Moravia, where in the 1740s he made the sacristy of Alt-Brünn's (Staré Brno) Augustinian church and the facade of Brünn's (Brno) St. Thomas church, as well as some minor works mostly in Znaim (Znojmo), recently attributed to him. He may be identical with a master registered as "Joseph Leonard Weber Loco Svejnicz", who obtained citizenship in Nagyszombat (Trnava) in 1749. His name can be found in Buda registers of birth from 1753, since his seven children were baptized here.

His sculptural activity is documented from 1757. His works are the stone sculptures of "Faith, Hope" and "Charity" above the portal of St. Anne's church from 1765, and the statue of "St. Florian" on the facade of the St. Florian Chapel, as well as the figures of the organ, high and side altar figures of the chapel (1761-66). These monuments of international Rococo fit appropriately in their aristic environment in Buda. Weber died in 1773, at the age of seventy-one. Another sculptor of the same name, who worked in Buda in 1784, was probably a son of the master, born in Neustadt (Prudnik) in 1738.