Please let us know how it goes. Weather, especially at a high altitude field like MEX, has a big impact on V speeds and W&B, but I've never heard of offloading after leaving the gate. Commercial aircraft don't push back until they've input pax, fuel, bags, etc, and confirmed the numbers with dispatch. On empty flights, you can get asked to move to the center of the plane for W&B, and obviously this occurs before pushing from the gate. Could have been a wind direction change between push back and takeoff that required shifting to a shorter runway. It also could have been an eff up in the cockpit, which would be a serious issue, W&B is a major safety input.