c. 1600, "boil gently," probably from caudle (n.) "warm drink for invalids" (c. 1300), from Anglo-French caudel (c. 1300), ultimately from Latin calidium "warm drink, warm wine and water," neuter of calidus "hot," from calere "be warm" (from PIE root *kele- (1) "warm").
The verb meaning "treat tenderly, make effeminate by pampering" first recorded 1815 (in Jane Austen's "Emma"), but the connection to the other word is uncertain; it might as well derive from caudle. Related: Coddled; coddling.