The weigh stations are only for commercial trucking. They check the bill of lading and the loading and unloading records, then compare them to the actual weight when you pull in. They are simply checking to make sure the trucks have not picked up or dropped off any non-recorded, illegal cargo, like untaxed cigarettes, alcohol, and other goods that might be transported/exported/imported state-to-state without paying the proper taxes.
Also - trucks are limited to the type and weight of cargo, depending on their licensing. It just keeps everyone honest. Now and again, you will see a police car parked there, in case they need to chase a truck down that tries to bypass the station. In Illinois, and many other states, trucks have a transponder in the windshield that is read by an overhead reader, ahead of the station. If they don't need to stop, the in-cab device indicates they can drive on by.
Travel trailers and other non-commercial towed vehicles need not stop. But don't feel like an idiot. I was worried about it, too, until someone explained it to me. Until I had my first camping trailer, I never gave it a thought.
2015 Jay Flight 32RLDS Elite
2012 Chevy 2500HD Crew Cab LTZ (6.6L Duramax/Allison)
Equalizer Hitch (1200# bars)