He received his education at the universities of Berlin, Vienna, and Breslau, graduating in 1868. After having taken part in the Franco-Prussian war as assistant surgeon he settled in Breslau, and for the following two years was assistant to Heinrich Waldeyer; from 1870 to 1874 to Lebert, and then to Cohnheim, who he followed to Leipzig in 1878. There he became assistant professor of pathology at the university in 1879. In 1884 he was appointed professor of pathological anatomy at the Senkenbergsche Stiftung in Frankfort-on-the-Main, and received the title of "Geheimer Medizinal-Rat" in 1899.
Weigert assisted Cohnheim in many of his researches, and wrote much on the staining of bacteria in microscopy. He contributed many essays to medical journals. Among his works are: "Zur Anatomie der Pocken" (Breslau, 1874); "Färbung der Bacterien mit Anilinfarben" (ib. 1875); "Nephritis" (Leipzig, 1879); "Fibrinfärbung" (1886); "Beiträge zur Kenntniss der Normalen Menschlichen Neuroglia" (Frankfort-on-the-Main, 1895); "Elastische Fasern" (ib. 1898).