I do believe most if not all states have a reciprocity effect that basically says they will honor other states licensing when traveling through their state. That is for privately owned not a commercial vehicle.
No reciprocity on weighted tags for non commercial vehicles according to my state size and weights folks. Just the fact that the truck has a registration is the only reciprocity. They say weighted registrations for a non commercial vehicle simply satisfies your states registration requirements. Keep in mind some states may have a single GVW or maybe a GCW or a laden or a tonnage or whatever a state calls it, to register a vehicle in that state. My state has no such weight requirements for any private use vehicle ..... just commercial.
Now if the vehicle has a "commercial registration" which require a GVW or GCW per fed requirements then registered wights have reciprocity between the states coast to coast and border to border.