The Middle English Dictionary identifies the word seurgate ("sewer-gate") in a 1403 text, and, soon after that, other sources show souer, seuer, and finally sewer emerging to describe channels for carrying away waste and drainage. All of this comes from the Anglo-French word sewere, which is from Old French sewiere or seuwiere. That's thought to be a pretty mangled borrowing from the unattested Gallo-Roman word exaquaria, which meant something more like "drain". The Latin roots there are glaringly obvious (and present in multiple English words): ex-, meaning "out", and aquarius, "pertaining to water" - so water is flowing outwards. Ex- is from Proto-Indo-European eghs, also "out", and aqua derives, through Proto-Italic akwa, from another PIE reconstruction, hekweh, which still meant "water".
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.