The word bra obviously comes from brassiere, and that comes from French brassiere, but here it gets interesting. In Old French, the etymon of these terms was braciere, and that referred to a protective lining of armor meant to protect the arm (yes, this is related to brace). Further back, the Old French word brace meant "arm", and that comes from Latin brachium, meaning "arm" as well (this is connected to several brachio- words, including bracelet, embrace, brachiosaurus, and, bizarrely, pretzel- we'll have to get into that later). In Greek, brakhion meant "upper arm", but before that, it meant "short", purportedly because the upper arm is shorter than the lower arm. What a strange metonymical switch! Further back, we can trace this to Ancient Greek brakhus, meaning "short" as well, and, through Proto-Hellenic, this derives from the reconstructed Proto-Indo-Europpean root mregus, "short" or "brief". For a short period in the 1940s, the word brassiere has been more commonly used than bra, but the latter form really took off since then, and currently stands at about nine times the usage of brassiere.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.