Weil studied medicine at the University of Heidelberg, and afterwards furthered his education in Berlin and Vienna.
In 1886, he was appointed professor of special pathology and therapy at the University of Dorpat, but resigned shortly afterwards, after contracting tuberculosis of the larynx and permanently losing his voice.
Later he lived and worked in Ospitaletto, San Remo and Badenweiler, relocating to Wiesbaden in 1893, where he died in 1916.
Among his written works was a treatise on the auscultation of arteries and veins, Die Auscultation der Arterien und Venen (1875), and a monograph titled Handbuch und Atlas der topographischen Percussion (Handbook and atlas of topographical percussion) (1877).
[1] Shortly after receiving news that Weil's disease was caused by a spirochete, he died of acute hemoptysis.