Now that I think about it some more, I don't think that spacetime expands, because spacetime includes all past and future times within it. So the balloon at a particular point in its expansion represents space, a cross section of spacetime. Then the balloon analogy is flawed in that it suggests that such a splitting is legitimate. But each point of the embedding space actually represents a point of spacetime, since the balloon will at some point in time contain that point of the embedding space.