I confess I had a mistaken thought that weigh stations were akin to toll booths. That is, that fees were levied based on the weight.

I can think of several problems with that thought, taking it longer, of course. :(

I'm FAR from an expert, but you aren't totally misguided. That was the original intent once upon a time, now it's more about safety. They do weigh trucks to ensure they aren't going to destroy a bridge or damage roads if they're overweight for their route - but they're primarily checking a driver's log book to ensure they aren't over hours, the truck passes safety inspections, the driver isn't transporting illicit goods, etc.