In Greek mythology, there exists the story of the hero, Perseus.
Perseus was known for having slain the Gorgon, Medusa, one of the three Gorgon sisters known for their beauty.
The goddess, Athena, transformed Medusa's appearance so that any man who looked upon her turned to stone (hence, the mission to slay her). According to the Greek storyteller, Ovid, the once beautiful Medusa was punished by Athena with a hideous appearance and loathsome snakes for hair for having been raped in Athena's temple by Poseidon. Punishment for having been raped -- not fair and not sensible.
There is a more sensible interpretation, one that fits common experience. Men are commonly "petrified" (turned to stone -- immobilized) by the appearance of a beautiful woman, so that they cannot approach her. This reaction may be an development of Nature to protect beautiful women from men. The snakes-for-hair in the Medusa story help "explain" why men turned to stone -- a literary device.
The "petrified" part goes with "head over heels", entranced.
When standing, most of our weight goes through our heels -- more or less centered around a place on the heel just behind where the little toe ends, but inward.
Off center is off-balance.
Balanced is centered.
Head-over-Heels is balanced, but not going anywhere.
However, it is a good position to go anywhere, from.
However, most people are off-center and off-balance, and so the term, "Head-over-Heels" has come to mean its opposite -- off-balance -- because, in the general vernacular, "Head-over-Heels" means, "in love". People apply it to themselves to signify feeling emotionally off-balance.
And There We Are -- another case of "inverted meanings".
Here's The Invertor for reversing "inverted meanings".
~ GO ~