Old English middel, "equally distant from extremes or limits; intermediate," from Proto-West Germanic *midla- (source also of Old Frisian middel, Old Saxon middil, Middle Low German, Dutch middel, Old High German mittil, German mittel), from Proto-Germanic *medj, from PIE root *medhyo- "middle."
Middle finger "the third finger" (counting the thumb as the first) so called from late Old English. Middle school is attested from 1838, originally "middle-class school, school for middle-class children;" the sense in reference to a school for grades between elementary and high school is from 1960. Middle management, the level below senior management, is by 1941.
Middle-of-the-road in the figurative sense is attested from 1894, originally political; edges of a dirt road can be washed out and thus are less safe, but the notion here probably is of the middle as "less exposed to ambush." Middle way in the figurative sense of "path of moderation" is from c. 1200. Middle ground as "place of moderation or compromise between extremes" is by 1961. Middle-sized "of medium size" is by 1620s.
In U.S. history, the Middle States (1784) were those between New England and the South (New York, New Jersey, Pennsylvania, Delaware). Middle America for "the 'silent majority,' the generally conservative middle class regarded as a homogeneous group" is by 1968.