'reeky' (Modern English adjective) comes from the verb 'reek' + adjectival suffix '-y'; 'reek' in Modern English comes from Old English 'rēoc' / Old Norse 'reyk' meaning 'smoke' or 'steam'.

'reeky' developed in Modern English as an adjective formed from Middle English 'reken'/'reken' or from the verb 'reek' (Middle English forms influenced by Old Norse/Old English roots); the element 'rēoc'/'reyk' meaning 'smoke' produced senses related to smell and steam that eventually gave rise to senses like 'foul smell', and the suffix '-y' formed the adjective 'reeky'.

Initially associated with 'smoke' or 'fuming' (literal sense of emitting smoke), the meaning broadened to denote a strong, unpleasant smell and then to figurative senses (strongly suggestive of something).