Both the noun and the verb are from older Germanic forms meaning “smoke”. That is a brutal oversimplification of an absolutely fascinating morning spent in the OED reading about the relationship of “reek” to Baltic words for various pickled foods. For serious, at 33 cents/day, an OED subscription is the coolest thing ever.

• 03.015 The faggots are reeking,
• 06.072 and through the reek he could see the goblins
• 11.011 all the halls within must be filled with his foul reek.’