It's possible it's a regional slang term or a creative, informal way of describing someone. However, without more context, it's impossible to determine its precise meaning.
If you encountered this phrase, it's best to ask the person who used it to clarify what they meant.
Perhaps they are referring to:
* Tears: Onions are known for making people cry when they are chopped. "Onion-eyed" could be a humorous way of saying someone is crying or is about to cry.
* Irritated Eyes: The fumes from chopping onions can irritate eyes. "Onion-eyed" could be used to describe someone with red, watery, or irritated eyes.
* A Figurative Meaning: Maybe it's a metaphor, where the onion layers represent something like deception or complexity, and the eyes are used to symbolize perception.
To understand the true meaning, more context is needed.