"toward and upon; to and in connection with; to the top of," 1580s, on to, from on + to. It appeared much later than parallel into, unto. As a closed compound, onto (on analogy of into), it is recorded from 1715. "The word is regarded by purists as vulgar, and is avoided by careful writers" [Century Dictionary, 1895].
"act of forming into regiments; state of being formed into classified systems," 1856, noun of action from regiment (v.).
1705, "to divide into classes, place in ranks or divisions," from class (n.) or French classer. Sense of "to place into a class" is from 1776. Related: Classed; classing.