Yours, Etc.: Origins and Uses of 8 Sign-Offs
1844, "full of kinks, twisted, curly," from kink + -y (2). Meaning "odd, eccentric, crotchety" is from 1859; that of "sexually perverted" is from 1959. Related: Kinkiness.
[the stronger fifth sense is said to have originated among British homosexuals in the 1920s]