I imagine they would use the concept of leverage so the balance point would not be in the center, but instead closer to the cow... You'd probably need some sort of harness to put the cow on. Then you load up weights on the other side until the cow and weights are nearly level. The weight of each individual weight is probably added up and then multiplied by some multiple dictated by how much leverage was granted by the difference in distances from the balance point. That should give you the weight of the cow. The reason for the leverage/multiple is because it doesn't make sense to have to lift a ton of weights to make it that same weight as the cow (its just impractical).
Anyways, that's all a guess. I would experiment.
