I quote only the germane sentences from Etymonline on 'even (adj.)':
The adverb is Old English efne "exactly, just, likewise."
Modern adverbial sense
([2.] introducing an extreme case of something more generally implied [End of 2.])
seems to have arisen 16c. from
[1.] use of the word to emphasize identity ("Who, me?" "Even you") [End of 1.].
Etymologists are uncertain whether the original sense was "level" or "alike."
Please see this question's title.
What semantic notions underlie 1 and 2?