Do you know if your 10' U-Haul will exceed 10 000 lbs? If you know, please edit your question.
I found this map on Pinterest.
I copy paste from U-Haul FAQ.
Do I need to stop at the weigh stations when driving a U-Haul truck?
The laws vary from state to state and throughout Canada. U-Haul customers moving their own household goods are typically not required to stop at weigh stations because it is not a commercial move. However, some states require that all trucks stop at the weigh stations. If in doubt, stop at the weigh station. You may want to check the rules of each state you are driving through beforehand.
Does My Moving Truck Need to Stop at a Weigh Station? | Moving.com
What states require rental trucks to stop at weigh stations?
Commercial vehicles are required to stop at weigh stations in the majority of states. However, only certain states also require that rental trucks carrying household goods (in other words: non-commercial trucks) stop at weigh stations. If the rental truck weighs over 10,000 lbs, it may need to stop at weigh stations in certain states. Below is a summary of the rules and laws surrounding trucks and weigh stations, according to the AAA Digest of Motor Laws and/or the state’s Department of Transportation.
I copy paste just your states in A to Z order.
Idaho – No
Montana – Yes
“Vehicles transporting agricultural products and trucks with a GVW of 8,000 lbs. or more and new or used RVs being transported to a distributor or dealer must stop.”
Washington – Yes
Wyoming – Yes
“Trucks are required to stop when instructed by a regulatory sign (black letters on a white background) or a police officer. Trucks and drivers are chosen for inspection on a random basis.”
What if I’m still not sure whether or not I need to stop at a weigh station?
When in doubt, we recommend stopping at a weigh station. After all, it’s better to be safe than sorry. If there’s no need for you to stop, the patrol officer will likely wave you through.