We often use just with recent times (e.g. "I've just arrived from the airport (5 minutes ago)") We sometimes use just in place of only, like Daniel said (e.g. "Just a little meat." he only had some meat") I'm not sure, but "only" usually implies exclusivity "She only eats meat" but we don't use just in that way and is more often used with time clauses: I just washed the floor (a few minutes ago) I only washed the floor (and I didn’t wash the table) Here are some more examples: http://www.espressoenglish.net/difference-between-just-and-only/

"She just eats meat." is incorrect English. It is correct to write "She only eats meat." In your example we may modify the intent of the clause by writing the question "What did you eat?" and answer the question "Just a little meat." The way that the word is used here is as an adverb.