Old English efen "level," also "equal, like; calm, harmonious; quite, fully; namely," from Proto-Germanic *ebnaz (cf. Old Saxon eban, Old Frisian even "level, plain, smooth," Dutch even, Old High German eban, German eben, Old Norse jafn, Danish jævn, Gothic ibns).
Etymologists are uncertain whether the original sense was "level" or "alike." Used extensively in Old English compounds, with a sense of "fellow, co-" (e.g. efeneald "of the same age;" Middle English even-sucker "foster-brother"). Of numbers, from 1550s. Modern adverbial sense (introducing an extreme case of something more generally implied) seems to have arisen 16c. from use of the word to emphasize identity ("Who, me?" "Even you," etc.) Sense of "on an equal footing" is from 1630s. Rhyming reduplication phrase even steven is attested from 1866; even break first recorded 1911. Even-tempered from 1875.
"to make level," Old English efnan (see even (adj.)).
"end of the day," Old English æfen, Mercian efen, Northumbrian efern (see eve).
Restored to balance and health; rational: ''I was really emotionally fucked up.'' ''Are you evened out now?'' (1970s+)
On the same footing: When you hit me we'll be even (1637+)