Both spellings of “eying” and “eyeing” are correct and acceptable to use in English writing. Both words indicate the same thing: that you are actively looking at someone or something. They denote a closer observance than normal with a sentiment of scrutiny.
It’s one of those words in English that go outside the normal rule of other words that follow the same spelling. The way it spells will mostly rely on where you are in the world. If you live in the United States, you’re likely to find it “eyeing.” But, in the UK, it will spell out as “eying.”
“Eying” is an optional and alternate means of spelling it. However, it’s best to use this in terms of the audience you’re writing for. If you know you have people from the UK who will be reading your words, then use “eying.” But, “eyeing” if they are American.
“Eyeing” for Grammar
That said, “Eyeing” is visually identifiable. This is a gerund and better for the brain and eyes to translate. However, most words ending in –e have a requirement to remove the –e before attaching the –ing. But, in the case of the word, “eye,” it’s optional.
The act of attaching –ing makes it become a present participle or gerund. This shifts the word from a noun into a verb. This then comes under verb conjugation rules. The good news is, nothing changes, the –ing remains regardless of the subject. But conjugation “to have” plus “been” or “to be” occur before it. This will largely depend on past or present references.
I am eyeing that beautiful necklace.
You are eying that woman over there, aren’t you?
He is eyeing that sports car.
She has been eyeing several colleges and still can’t decide.
We have been eyeing that house.
They have been eying each other.
Whether you want to use “eyeing” or “eying,” it doesn’t really much matter. But, it is easier on the reader’s eyes if you use “eyeing.” It’s a precise and concise way to say someone is looking at another person or object with a certain amount of scrutiny.