Steve, the limbs were balancing the pull for the entire process. You pulled to the weight with movement on one limb. As you thinned the other, it move until it balanced the other limb with that other limb pulled to right where it was the first pull. If you had hooked the bow string on a nail in the wall and anchored the handle so it would not tip, your bending limb would have behaved and weighed exactly what you measured at the beginning.
Here's another balancing paradox. Howard Hill once took two 60# bows with their strings within the other's. He took a handle in each hand in front of him and spread his arms until both bows were draw between his hands. Those telling the story said he was pulling 120#. NOPE. He was pulling 60#, because that's all it took to bring either bow to full draw.