watch like a hawk
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.
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The American Heritage® Idioms Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.