tick: English now has no fewer than four distinct words tick in general use. The oldest, tick ‘mite’ [OE], comes from a prehistoric West Germanic *tik-, which may be related to Armenian tiz ‘bug’. Tick ‘sound of a clock, mark of correctness, etc’  originally meant broadly ‘light touch, tap’; its modern uses are secondary and comparatively recent developments (‘sound of a clock’ appears to have evolved in the 16th century, and ‘mark of correctness’ did not emerge until the 19th century). Tickle  is probably a derivative. Tick ‘mattress case’  was borrowed from Middle Dutch tēke, which went back via Latin thēca to Greek thékē ‘cover, case’.
And tick ‘credit’  (as in on tick) is short for ticket. => tickle; ticket
parasitic blood-sucking arachnid animal, Old English ticia, from West Germanic *tik- (cognates: Middle Dutch teke, Dutch teek, Old High German zecho, German Zecke "tick"), of unknown origin, perhaps from PIE *deigh- "insect." French tique (mid-15c.), Italian zecca are Germanic loan-words.
mid-15c., "light touch or tap," probably from tick (v.) and cognate with Dutch tik, Middle High German zic, and perhaps echoic. Meaning "sound made by a clock" is probably first recorded 1540s; tick-tock as the sound of a clock is recorded from 1845.
early 13c., "to touch or pat," perhaps from an Old English verb corresponding to tick (n.2), and perhaps ultimately echoic. Compare Old High German zeckon "to pluck," Dutch tikken "to pat," Norwegian tikke "touch lightly." Meaning "make a ticking sound" is from 1721. Related: Ticked; ticking.
To tick (someone) off is from 1915, originally "to reprimand, scold." The verbal phrase tick off was in use in several senses at the time: as what a telegraph instrument does when it types out a message (1873), as what a clock does in marking the passage of time (1777), to enumerate on one's fingers (1899), and in accountancy, etc., "make a mark beside an item on a sheet with a pencil, etc.," often indicating a sale (by 1881, from tick (n.2) in sense "small mark or dot"). This last might be the direct source of the phrase, perhaps via World War I military bureaucratic sense of being marked off from a list as "dismissed" or "ineligible." Meaning "to annoy" is recorded by 1971.