1
general::
Ogle, flirt with, as in To her sister's disgust, she was always making eyes at the boys. Although slightly different versions, such as throw the eye at, are much older, this precise locution was first recorded in William Makepeace Thackeray's Henry Esmond (1852): "She used to make eyes at the Duke of Marlborough." See Also GIVE SOMEONE THE ONCE-OVER.
American Heritage Idioms
2
general::
Phrase(s): make eyes at someone
Fig. to flirt with someone. • Mother, he’s making eyes at me! • Jed tried to make eyes at all the young women.
McGrawhill's American Idioms And Phrasal Verbs