Son of Johann Michel Wegely (d. 1755) and Anna Choptka Höggeri (d. 1750). Married (1741) to Maria Charlotte Von Der Burg (b. 1721). Originally a wool-manufacturer, in 1751 he founded the first porcelain factory in Berlin. However, during the seven years war, when Prussia occupied Dresden, including the nearby city of Meissen and it's more famous porcelain factory, competition became too fierce, and Wegely stopped operations in 1757.1
Boswell went to Wegely's campagne, near Charlottenburg Castle in Berlin, on July 21, 1764, in the company of C. F. Hübner and others. It is unclear whether he actually met Wegely on this occasion, as his journal isn't specific on this point. The next day, however, he dined "with our family" (presumably the Kircheisens) at Monsieur Wegely's.
Wegely died less than two months later, aged just 49.
In 1978 was published Gisela Zick's Berliner Porzellan der Manufaktur von Wilhelm Caspar Wegely 1751 - 1757 which is sometimes available via AbeBooks.