Old English efen "level," also "equal, like; calm, harmonious; equally; quite, fully; namely," from Proto-Germanic *ebna- (source also of Old Saxon eban, Old Frisian even "level, plain, smooth," Dutch even, Old High German eban, German eben, Old Norse jafn, Danish jævn, Gothic ibns). The adverb is Old English efne "exactly, just, likewise." 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").
Etymologists are uncertain whether the original sense was "level" or "alike." Used extensively in Old English compounds, with a sense of "fellow, co-" (as in efeneald "of the same age;" Middle English even-sucker "foster-brother"). Of numbers, from 1550s. Sense of "on an equal footing" is from 1630s. Rhyming reduplication phrase even steven is attested from 1866; even break (n.) first recorded 1907. Even-tempered from 1712. To get even with "retaliate upon" is attested by 1833.
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.
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Definitions of evenly from WordNet
in equal amounts or shares; in a balanced or impartial way;