Angels
I was reading the long thread about the scale at the end of the film and it seems like hardly anyone at all picked up on the angel imagery. It's not just that he was practicing at being a "ghost" - he was becoming an angel in more ways than one.
When he was in jail, he stuck his arms out and behind him, waving his wrists lightly, as if they were wings.
In the final scene, when she's trying to find him and she holds her arms out to block him from darting away, their bodies create the shadow of an angel on the wall.
When they're on the scale, it measures zero because, essentially, they're not on the ground. It's where the movie's symbolism crosses over into the "physical world." She didn't fix the scale to match both their weights (she fixed it earlier, demonstrating what she picked up from him, because it measured her own weight wrong) and they didn't "balance each other out" because weighing a negative amount doesn't make any sense (and he weighs more than her anyway).
Also keep in mind all the good deeds he had done earlier. The guy acts as a guardian angel of sorts, or at least he perhaps aspires to it. I don't intend for that to be taken literally as the point of the movie, but I'm saying that this "angel" imagery and symbolism is laid throughout the movie.