Old English cearful "mournful, sad," also "full of care or woe; anxious; full of concern" (for someone or something), thus "applying attention, painstaking, circumspect" (late Old English), the main modern sense; from care (n.) + -ful. In Middle English also "miserable, unfortunate," of persons or things; "causing fear, frightening, terrible." Careful-bed (early 14c.) was "sick-bed;" careful-day (c. 1200) was "judgment day."
Dragons dryfes doun
With kene carefull crie.
["The Wars of Alexander," c. 1400]
Old English cearig "sorrowful, full of care," the adjective from care (n.), q.v. Sense evolved 16c. from "full of care" to "careful." Compare the sense evolution of careful. Meaning "sparing, frugal" is from 1560s. Cognate with Old Saxon carag, Old High German charag "full of sorrow, trouble, or care." Related: Charily; chariness.