If I had to guess I'd say Elves had Celtic origins, close to those of Irish and Scottish fairies. In the Middle Ages and earlier fairies were thought of as full-sized and very beautiful beings, also very frightening and powerful. They weren't intrinsically evil, but they belonged to an older (read: pre-Christian) world and any human who got entangled with them would either disappear forever (like in "The Child Who Went With the Fairies") or at least be changed drastically by the fact that fairies lived outside of normal time (like all those fairy-tales about the man who goes to dance one reel with a fairy party and at the end of the reel returns home and it's a hundred years later).
Sounds a lot like those lines about "Men say that few escape the snares of the Sorceress of the Golden Wood" and the fact that time passes differently in Elven-country. And since Tolkien's Elves don't engage in baby-stealing or luring people away for the fun of it, who knows, maybe the medieval fairies got a bad rap. That'll happen when people think you're strange.
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Father, dear Father, if you see fit, We'll send my love to college for one year yet
Tie blue ribbons all about his head, To let the ladies know that he's married.
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