Eyeing or Eying

Okay, according to what I've researched online, they are apparently both (mostly) acceptable. Most dictionary sites will take include either spelling, though there are a few that say "eyeing" is incorrect. This is just mind-boggling, to me. I never *ever* saw the word spelled "eying" until a bandom story. At first I thought it was a typo and dismissed it. Then I read it in another bandom fic, and another. The thing is, one of my majors is English Literature, and I've read a tonne of novels, taken tonnes of classes on the English language, and I never saw it. Or it never caught my eye, which seems unlikely, since the spelling is so glaringly wrong (to me) that I don't think I could ignore it.
So, does anyone know why there are two different spellings? Is it a regional thing? Is one more correct than the other?