Sally and The Doctor in “Blink”

What do you mean, Angels? You mean those statue things?

Creatures from another world.

But they're just statues.

Only when you see them.

What does that mean?

The "Lonely Assassins", they used to be called. No one quite knows where they came from, but they're as old as the universe, or very nearly, and they have survived this long because they have the most perfect defence system ever evolved: they're quantum-locked. They don't exist when they're being observed. The moment they are seen by any other living creature, they freeze into rock. No choice, it's a fact of their biology. In the sight of any living thing, they literally turn to stone. And you can't kill a stone. Of course, a stone can't kill you either, but then you turn your head away, then you blink... and oh, yes it can.

[to Larry, regarding a nearby Angel] Don't take your eyes off that.

That's why they cover their eyes. They're not weeping, they can't risk looking at each other. Their greatest asset is their greatest curse. They can never be seen. The loneliest creatures in the universe.