From eye + ball.

eyeball (plural eyeballs)

1. The ball of the eye.
   • 1610–1611 (date written), William Shakespeare, “The Tempest”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, →OCLC ↗, [Act I, scene ii], page 4 ↗, column 2:

     Goe make thy ſelfe like a Nymph o' th' Sea.
     Be ſubiect to no ſight but thine, and mine: inuisible
     To euery eye-ball elſe: goe take this ſhape,
     And hither come in't: goe: hence
     With diligence.

2. A person's focus of attention.
3. (informal) Surveillance.
   • 2016, Marie Breen-Smyth, The Ashgate Research Companion to Political Violence, page 384:

     Intelligence work is necessarily limited in scope by the capacity of national surveillance systems. […] Ultimately, it is only when you have an 'eyeball' or the electronic equivalent on a suspect that you have a reasonable chance of a preventive intervention.

4. (marketing, in the plural) A readership or viewership.

   We need compelling content for the new Web site so we can attract more eyeballs.

5. (CB radio, slang) A face-to-face meeting.

   We had an eyeball last year.

6. (Caribbean) A favourite or pet; the apple of someone's eye.

• eye-apple

• French: globe oculaire
• German: Augapfel
• Italian: bulbo oculare
• Portuguese: globo ocular
• Russian: глазно́е я́блоко
• Spanish: globo ocular

eyeball (eyeballs, present participle eyeballing; simple past and past participle eyeballed)

1. (transitive, informal) To gauge, estimate or judge by eye, rather than measuring precisely; to look or glance at.

   A good cook can often just eyeball the correct quantities of ingredients.

   Each geometric construction must be exact; eyeballing it and getting close does not count.

2. (transitive, informal) To stare at intently.

   Are you eyeballing my girl?

3. (intransitive) To roll one's eyes.

• French: évaluer à vue de nez, évaluer au pif, faire à la louche
• German: nach Augenmaß abschätzen, nach Augenmaß abmessen, nach Augenmaß hinzugeben, nach Augenmaß hinzufügen