Green’s Dictionary of Slang

eat up v.

1. [mid-19C–1950s] to scold or rebuke.

2. [mid-19C+] to defeat or destroy.

3. [late 19C+] (also eat) to believe unquestioningly.

4. [1900s–10s] to do well; to act competently; to deal with efficiently.

5. [1910s+] (orig. theatre, also eat) to enjoy immensely, to acclaim.

6. [1930s+] to take control of, to ‘consume’.

In phrases

wouldn’t that eat you up?

[1910s] (US) phr. implying infuriation .