I keep seeing this one all over the Internet as an example of one of those "immovable object meeting irresistible force" paradoxes, so I thought I should address it here.
This really wouldn't last long.
If the Weeping Angel and the Silence looked at each other, the Weeping Angel would be frozen in place until the Silence looked away. At that point, the Weeping Angel can move, and it can still see the Silence, so it wouldn't forget the Silence. It'd just charge up to it and zap it back in time 80 years or so.
At that point, it would perhaps wonder why it felt so full, but it wouldn't be much of a contest.