'reek' originates from Old Norse, specifically the word 'reykja', where 'reyk' meant 'smoke'.

'reek' entered Middle English influenced by Old Norse 'reykja' (and related Germanic forms) and developed into the modern English word 'reek'.

Initially it meant 'to emit smoke' or related to 'smoke'; over time it broadened to mean 'to give off a strong, unpleasant smell' and, figuratively, 'to be strongly characterized by' something.