keep a beady eye on somebody/something
keep (one's)/a beady eye on (someone or something)
To watch something very closely or carefully; to be particularly attentive to or vigilant about something. Used especially when one is distrustful or overly protective. The toddler kept a beady eye on his toys throughout the party, screaming at any child who dared to play with his things. One of the most difficult aspects of trying to curb the issue for law enforcement is that it's impossible for them to keep their beady eye on every corner of the internet at once.