tick (n.1) Look up tick at Dictionary.com
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.
tick (n.2) Look up tick at Dictionary.com
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.
tick (v.) Look up tick at Dictionary.com
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.
tick (n.3) Look up tick at Dictionary.com
"credit," 1640s, shortening of ticket (n.).