Words related to garrulous
Old English carian, cearian "be anxious or solicitous; grieve; feel concern or interest," from Proto-Germanic *karo- "lament," hence "grief, care" (source also of Old Saxon karon "to lament, to care, to sorrow, complain," Old High German charon "complain, lament," Gothic karon "be anxious"), said to be from PIE root *gar- "cry out, call, scream" (source also of Irish gairm "shout, cry, call;" see garrulous).
If so, the prehistoric sense development is from "cry" to "lamentation" to "grief." A different sense evolution is represented in related Dutch karig "scanty, frugal," German karg "stingy, scanty." It is not considered to be related to Latin cura. Positive senses, such as "have an inclination" (1550s); "have fondness for" (1520s) seem to have developed later as mirrors to the earlier negative ones.
To not care as a negative dismissal is attested from mid-13c. Phrase couldn't care less is from 1946; could care less in the same sense (with an understood negative) is from 1955. Care also has figured since 1580s in many "similies of indifference" in the form don't care a _____, with the blank filled by fig, pin, button, cent, straw, rush, point, farthing, snap, etc., etc. Related: Cared; caring.
1580s, from French garrulité, from Latin garrulitatem (nominative garrulitas) "chattering, loquacity," from garrulus "talkative" (see garrulous).
1520s, "to make a brief, harsh, grating sound," often in reference to bird screeches; the word often is said to be echoic or imitative; compare jargon (n.), jay (n.), garrulous. Figurative sense of "have an unpleasant effect on" is from 1530s; that of "cause to vibrate or shake" is from 1560s. Related: Jarred; jarring. As a noun in this sense from 1540s.
1670s, earlier slogorne (1510s, Gavin Douglas), "battle cry," from Gaelic sluagh-ghairm "battle cry used by Scottish Highland or Irish clans," from sluagh "army, host, slew," from Celtic and Balto-Slavic *slough- "help, service." Second element is gairm "a cry" (see garrulous). The metaphoric sense of "distinctive word or phrase used by a political or other group" is attested from 1704 (as slughon). The spellings also included a fully folk-etymologized slughorn.