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1520s, "but prob. in popular use from an earlier period" [OED], likely from tops, plural of top (n.1) "highest point" + obsolete terve "turn upside down, topple over," from Old English tearflian "to roll over, overturn," from Proto-Germanic *terbanan (cf. Old High German zerben "to turn round"). The Century Dictionary (1902) calls it "A word which, owing to its popular nature, its alliterative type, and to ignorance of its origin, leading to various perversions made to suggest some plausible origin, has undergone, besides the usual variations of spelling, extraordinary modifications of form." It lists 31 variations.
Disordered; upside down (1528+)