The Doctor Who episodes "Time of the Angels" and "Flesh and Stone".
You know, the one where Amy had to keep her eyes shut, or the Weeping Angels would kill her?
Is this movie a ripoff of that?
It's been a while, but I'm pretty sure it's the exact opposite with the Weeping Angels.
They kill you when you STOP looking at them.
As for the general concept of "not looking at the monster or you'll die", it's nothing new.
There's Medusa and also that story with the salt pillars from way back when.
Apparently you missed their return episodes ("Time of the Angels" and "Flesh and Stone"), where Amy got a speck of Weeping Angel caught in her eye or something and had to keep her eyes closed or she'd die. So she had to spend ages stumbling through peril with her eyes kept closed.
Not my favorite episodes, but it sounds like someone found them... inspiring.