1
general::
Observe very closely, as in I was watching him like a hawk, but I never did see him take your wallet. This simile alludes to the hawk's exceptionally keen sight.
American Heritage Idioms
2
general::
Phrase(s): watch someone or something like a hawk
Fig. to watch someone or something very carefully. • The teacher watched the pupils like a hawk to make sure they did not cheat on the exam. • We had to watch our dog like a hawk in case he ran away.
McGrawhill's American Idioms And Phrasal Verbs