Green’s Dictionary of Slang

eat cheese v.1

[SE eat + SE cheesy; i.e. the quality of one’s smiles]

1. [1940s+] (orig. US black) to toady to, to ingratiate oneself with.

2. [1950s+] (US) to inform on, to betray; thus cheese-eating n.

3. [1970s] (US black) to be in love.