"exceed in any excess of evil," from Shakespeare's it out-Herods Herod in Hamlet's instruction to the players in "Hamlet" Act III, Scene II. Shakespeare used the same construction elsewhere ("All's Well that Ends Well" has out-villain'd villany). The phrase reflects the image of Herod as stock braggart and bully in old religious drama. The form of the phrase was widely imitated 19c. and extended to any excessive behavior.
Oh, it offends me to the soul to hear a robustious periwig-pated fellow tear a passion to tatters, to very rags, to split the ears of the groundlings, who for the most part are capable of nothing but inexplicable dumb-shows and noise: I would have such a fellow whipped for o'erdoing Termagant; it out-herods Herod: pray you, avoid it. ["Hamlet"]
1590s, "a 'vocal gesture' expressing the action of puffing anything away" [OED], used as an exclamation of dislike, scorn, or contempt, first attested in Hamlet Act I, Scene III, where Polonius addresses Ophelia with, "Affection! pooh! you speak like a green girl, / Unsifted in such perilous circumstance. / Do you believe his tenders, as you call them?" But the "vocal gesture" is perhaps ancient.
mid-13c., "something heavy; heaviness," from heavy (adj.). Theatrical sense of "villain" is 1880, short for heavy villain (1843), heavy leading man (1849) or similar phrases.
A "heavy business man," he who performs such parts as Ferardo in the Wife, the Ghost in Hamlet, and Malec, Edmund, Banquo, Buckingham and the principal villains of the drama, [will command at present] from $15 to $20 [per week]. ["The Amateur, or Guide to the Stage," Philadelphia, 1851]
late 14c., "inhabited place larger than a hamlet but smaller than a town," from Old French vilage "houses and other buildings in a group" (usually smaller than a town), from Latin villaticum "farmstead" (with outbuildings), noun use of neuter singular of villaticus "having to do with a farmstead or villa," from villa "country house" (from PIE root *weik- (1) "clan"). As an adjective from 1580s. Village idiot is recorded from 1825. Related: Villager (1560s).
"destination," 1520s, from French borne, apparently a variant of bodne "limit, boundary, boundary stone" (see bound (n.1)). Used by Shakespeare in Hamlet's soliloquy (1602) and elsewhere, from which it entered into English poetic speech. He meant it probably in the correct sense of "boundary," but it has been taken to mean "goal" (Wordsworth, Matthew Arnold) or sometimes "realm" (Keats).
The dread of something after death, The vndiscouered Countrey; from whose Borne No Traueller returnes. ["Hamlet" III.i.79]