From Middle English care, from Old English caru, ċearu (“care, concern, anxiety, sorrow, grief, trouble”), from Proto-Germanic *karō (“care, sorrow, cry”), from Proto-Indo-European *ǵār-, *gÀr- (“voice, exclamation”). Cognate with Old Saxon cara, kara (“concern, action”), Middle High German kar (“sorrow, lamentation”), Icelandic kör (“sickbed”), Gothic (kara, “concern, care”). Related also to Dutch karig (“scanty”), German karg (“sparse, meagre, barren”). See chary.
From Wiktionary
From Middle English caren, carien, from Old English carian (“to sorrow, grieve, be troubled, be anxious, to care for, heed”), from Proto-Germanic *karōną (“to care”), from Proto-Indo-European *ǵār-, *gÀr- (“voice, exclamation”). Cognate with Middle High German karn (“to complain, lament, grieve, mourn”), Alemannic German karen, kären (“to groan, wheeze, give a death rattle”), Swedish kära (“to fall in love”), Icelandic kæra (“to care, like”), Gothic (karōn, “to be concerned”).
From Wiktionary
Middle English from Old English cearu
From American Heritage Dictionary of the English Language, 5th Edition