When you're moving yourself or family using a U Haul trailer or U Haul truck you're not considered to be driving commercial.
Only commercial trucks that are moving goods and moving people for commercial purposes must stop at weigh stations.
So no you do not have to stop at a weigh station when you're driving a U Haul truck or pulling a U Haul trailer so you can just pass on by the weigh stations without needing to stop at them.
Only if you're driving a commercial truck or moving people commercially for hire then you need to stop at a weigh station.
But since you're just moving yourself with the U Haul trailer or U Haul truck there's no legal requirement to stop at a weigh station.