Etymology
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Words related to better

best (adj.)

Old English beste, reduced by assimilation of -t- from earlier Old English betst "of the highest quality or standing, first, in the best manner." This originally was the superlative of bōt "remedy, reparation" (Middle English bote "advantage, help, profit"), a word now surviving in its simple form only in the expression to boot (see boot (n.2)). Its comparative, better, and superlative, best, have been transferred to good (and in some cases well).

Old English bōt is from Proto-Germanic root *bat-, with comparative *batizon and superlative *batistaz. The superlative form is the source also of Old Frisian, Old Saxon, Middle Dutch best, Old High German bezzist, German best, Old Norse beztr, Gothic batists. Also in Old English as an adverb, "in the most excellent manner."

The best-laid schemes o' mice an' men
     Gang aft agley,
An' lea'e us nought but grief an' pain,
     For promis'd joy!
[Burns, from "To a Mouse, on Turning Her Up in Her Nest With the Plough, November, 1785"]

From late Old English as "of greatest advantage, most suitable." Best-seller as short for "best-selling book" is from 1889, apparently originally in the publishing trade; best friend was in Chaucer (late 14c.). Best girl is first attested 1881, American English; best man is 1814, originally Scottish, replacing groomsman.  

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good (adj.)
Origin and meaning of good

Old English gōd (with a long "o") "excellent, fine; valuable; desirable, favorable, beneficial; full, entire, complete;" of abstractions, actions, etc., "beneficial, effective; righteous, pious;" of persons or souls, "righteous, pious, virtuous;" probably originally "having the right or desirable quality," from Proto-Germanic *gōda- "fitting, suitable" (source also of Old Frisian god, Old Saxon gōd, Old Norse goðr, Middle Dutch goed, Dutch goed, Old High German guot, German gut, Gothic goþs). A word of uncertain etymology, perhaps originally "fit, adequate, belonging together," from PIE root *ghedh- "to unite, be associated, suitable" (source also of Sanskrit gadh- "seize (booty)," Old Church Slavonic godu "favorable time," Russian godnyi "fit, suitable," Lithuanian goda "honor," Old English gædrian "to gather, to take up together").

Irregular comparative and superlative (better, best) reflect a widespread pattern in words for "good," as in Latin bonus, melior, optimus.

Sense of "kind, benevolent" is from late Old English in reference to persons or God, from mid-14c. of actions. Middle English sense of "holy" is preserved in Good Friday. That of "friendly, gracious" is from c. 1200. Meaning "fortunate, prosperous, favorable" was in late Old English. As an expression of satisfaction, from early 15c. Of persons, "skilled (at a profession or occupation), expert," in late Old English, now typically with at; in Middle English with of or to. Of children, "well-behaved," by 1690s. Of money, "not debased, standard as to value," from late 14c. From c. 1200 of numbers or quantities, "large, great," of time or distance, "long;" good while "a considerable time" is from c. 1300; good way "a great distance" is mid-15c.

Why then, can one desire too much of a good thing. ["As You Like It"]

As good as "practically, virtually" is from mid-14c.; to be good for "beneficial to" is from late 14c. To make good "repay (costs, expenses), atone for (a sin or an offense)" is from late 14c. To have a good mind "have an earnest desire" (to do something) is from c. 1500. Good deed, good works were in Old English as "an act of piety;" good deed specifically as "act of service to others" was reinforced early 20c. by Boy Scouting. Good turn is from c. 1400. Good sport, of persons, is from 1906. The good book "the Bible" attested from 1801, originally in missionary literature describing the language of conversion efforts in American Indian tribes. Good to go is attested from 1989.

bettor (n.)
"one who lays a wager," c. 1600, also better, agent noun from bet (v.). The form is unusual; OED notes that English agent nouns in -er tend to shift toward -or as their senses become more specific; in this case it also could be to avoid confusion with better (n.1).
betterment (n.)
"improvement," 1590s, from better (v.) + -ment.
bet (n.)
1590s, "the mutual pledging of things of value to be won or lost based on some future event," appearing simultaneously with the verb, originally in the argot of petty criminals, a word of unknown origin. Perhaps a shortening of abet or else from obsolete beet "to make good" (related to better). The original notion is perhaps "to improve" a contest by wagering on it, or to encourage a contestant. Or perhaps the word is from the "bait" sense in abet. Meaning "that which is wagered" is from 1796.
bettermost 
"best," 1762, from better (adj.) + -most.
boot (n.2)

"profit, use," Old English bot "help, relief, advantage; atonement," literally "a making better," from Proto-Germanic *boto (see better (adj.)). Compare Old Frisian bote "fine, penalty, penance, compensation," German Buße "penance, atonement," Gothic botha "advantage, usefulness, profit." Now mostly in phrase to boot (Old English to bote), indicating something thrown in by one of the parties to a bargain as an additional consideration.

-er (2)

comparative suffix, from Old English -ra (masc.), -re (fem., neuter), from Proto-Germanic *-izon (cognates: Gothic -iza, Old Saxon -iro, Old Norse -ri, Old High German -iro, German -er), from PIE *-yos-, comparative adjective suffix. Originally also with umlaut change in stem, but this was mostly lost in Old English by historical times and has now vanished (except in better and elder).

For most comparatives of one or two syllables, use of -er seems to be fading as the oral element in our society relies on more before adjectives to express the comparative; thus prettier is more pretty, cooler is more cool [Barnhart].