The Fomorians once ruled Ireland. Their greatest king was Balor of the evil eye, because he could kill those on whom he looked in anger with his one eye - an early version of the X-men's Cyclops in fact. When he was old, his vast eyelid drooped, and had to be lifted by ropes and pulleys by his men. Now that's what I call a treatment for ptosis! Nowadays we just do a blepharoplasty.
Balor seems to be just one of a number of fearsome individuals with the ability to slay with a glance, like the basilisk (or cockatrice) and the gorgon Medusa. There's also Dracula who mesmerises his victims so that he can partake of their blood.
There seems to be an underlying fear about meeting a foe who can kill in this way. Think how helpless you would feel if faced with such an entity, unless you were Perseus, armed with a mirrored shield allowing you to fight your enemy without looking directly into their evil eye.
Balor is described as having a single eye, but this is a badge of godhood. Odin and Horus both lost an eye. The heiroglyph for Osiris is an eye above a throne, and the depiction of God on a dollar bill is an all-seeing eye above a truncated pyramid.
Thunderbolts were made by the cyclopses - another connection between the single eye and destruction. And let's not forget the most evil eye of all, Tolkein's Sauron.
The eye has often been described as the window of the soul, and I suppose that if the soul is evil, the the eye is too.