Sounds like skin tags - I've got them on my thighs and underarms but
not my eyelids.
http://www.nlm.nih.gov/medlineplus/ency/article/000848.htm

Are they yellow?  Do you have high cholesterol?  Could be xanthomas. A
co-worker years ago had some on his eyelids (although the article here
doesn't indicate that a common location)  
http://www.nlm.nih.gov/medlineplus/ency/article/001447.htm

Never heard of either one popping up overnight, though.  Usually when
I'm getting a new skin tag, it feels like a pimple is coming on and
then the tag gradually grows.  Ugly as all get out, but can't afford to
have them removed (insurance considers it "cosmetic")

Sherry

A "fold" that has "diameter"?  Well, if that is like another example I
saw (tiny flat protrusions), here is a cautionary tale of a naive
persons trials and errors with them.  1) clipping one off flush - OW!
Had a nerve bundle and blood supply, and left a lasting little scar.
2) clipping off the "dead" tip - ok but not as attractive as hoped and
any of this clipping probably very risky to eye if reflexes twitch at
wrong time.  3) leave alone - some do shrink away with time (maybe
others don't; haven't kept track).