Etymology
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tip (n.1)
c. 1400, "extreme end of something, top of something round or pointed, metal attachment to the end of something," from Middle Low German or Middle Dutch tip "utmost point, extremity, tip" (compare German zipfel, a diminutive formation); or from a Scandinavian source (compare Old Norse typpi).
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tip (v.1)
c. 1300, "to knock down, overturn, topple, knock askew" (transitive), of uncertain origin, possibly from Scandinavian (compare Swedish tippa "to tip, dump"), or from a special use of tip (n.). Intransitive sense of "to fall over, be overturned" is from mid-15c. Related: Tipped; tipping. To tip the scales at "weigh (so much" is from 1879. Tipping point attested by 1972. To tip (one's) hand "reveal one's intentions" is from 1907, an image from poker-playing.
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tip (v.3)
c. 1200, "to strike, occur suddenly," of uncertain origin, possibly from Low German tippen "to poke, touch lightly," related to Middle Low German tip "end, point," and thus connected to tip (n.); or else related to tap (v.1). Meaning "strike sharply but lightly" is from 1560s. Sports sense is from 1816, originally in cricket. Related: Tipped; tipping.
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over- 

word-forming element meaning variously "above; highest; across; higher in power or authority; too much; above normal; outer; beyond in time, too long," from Old English ofer (from PIE root *uper "over"). Over and its Germanic relations were widely used as prefixes, and sometimes could be used with negative force. This is rare in Modern English, but compare Gothic ufarmunnon "to forget," ufar-swaran "to swear falsely;" Old English ofercræft "fraud."

In some of its uses, moreover, over is a movable element, which can be prefixed at will to almost any verb or adjective of suitable sense, as freely as an adjective can be placed before a substantive or an adverb before an adjective. [OED]

Among the old words not now existing are Old English oferlufu (Middle English oferlufe), literally "over-love," hence "excessive or immoderate love." Over- in Middle English also could carry a sense of "too little, below normal," as in over-lyght "of too little weight" (c. 1400), overlitel "too small" (mid-14c.), overshort, etc.

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tip (n.2)
"a light, sharp blow or tap," mid-15c., from tip (v.3).
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tip (v.4)
"put a tip on, adorn with a tip," late 14c., from tip (n.) or Old Norse typpa. Related: Tipped; tipping.
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tip (v.2)

"give a small present of money to," c. 1600, originally "to give, hand, pass," thieves' cant, perhaps from tip (v.3) "to tap." The meaning "give a gratuity to" is first attested 1706. The noun in this sense is from 1755; the noun meaning "piece of confidential information" is from 1845; and the verb in the sense "give private information to" is from 1883.

The popularity of the tale of the word's supposed origin as an acronym in mid-18th century English taverns seems to be no older than Frederick W. Hackwood's 1909 book "Inns, Ales and Drinking Customs of Old England," where it was said to stand for To insure promptitude (in the form to insure promptness the anecdote is told from 1946). A reviewer of the book in The Athenaeum of Oct. 2, 1909, wrote, "We deprecate the careless repetition of popular etymologies such as the notion that "tip" originated from an abbreviated inscription on a box placed on the sideboard in old coaching-inns, the full meaning of which was "To Insure Promptitude." Also see here.

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over (prep., adv.)

Old English ofer "beyond; above, in place or position higher than; upon; in; across, past; more than; on high," from Proto-Germanic *uberi (source also of Old Saxon obar, Old Frisian over, Old Norse yfir, Old High German ubar, German über, Gothic ufar "over, above"), from PIE root *uper "over."

As an adjective from Old English uffera. The senses of "past, done,  finished; through the whole extent, from beginning to end" are attested from late 14c. The sense of "so as to cover the whole surface" is from c. 1400. Meaning "leaning forward and down" is from 1540s. The meaning "recovered from" is from 1929. In radio communication, it is used to indicate the speaker has finished speaking (1926).

Above expresses greater elevation, but not necessarily in or near a perpendicular direction; over expresses perpendicularity or something near it: thus, one cloud may be above another, without being over it. Over often implies motion or extension where above would not; hence the difference in sense of the flying of a bird over or above a house, the hanging of a branch over or above a wall. In such uses over seems to represent greater nearness. [Century Dictionary]

Phrase over and above (mid-15c.) is pleonastic, for emphasis. Adjective phrase over-the-counter is attested from 1875, originally of stocks and shares. To be (someone) all over "be exactly what one expects of (someone)" is by 1721.

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finger-tip (n.)
also fingertip, 1817, from finger (n.) + tip (n.). Related: Fingertips. To have something at one's fingertips is from 1870.
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tip-top (n.)
"extreme top," 1702, from tip (n.1) + top (n.1). Hence, "most excellent."
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