Category "weak-ptr"

Why can't a weak_ptr be constructed from a unique_ptr?

If I understand correctly, a weak_ptr doesn't increment the reference count of the managed object, therefore it doesn't represent ownership. It simply lets you

When is std::weak_ptr useful?

I started studying smart pointers of C++11 and I don't see any useful use of std::weak_ptr. Can someone tell me when std::weak_ptr is useful/necessary?