always reproducible
When you pull up the jobs list at the freight market, each job starts with a default type of trailer with a default weight/profit etc for that type of trailer, but you can change the trailer by clicking the little cog at the bottom of the job, which changes the weight/profit of the job too. If you do change the trailer, the weigh stations will still weigh the cargo from the default job.
Here's an example:
First the weight of my truck, fully fueled, 19,589 pounds.

The default job I want to take, highlighted in yellow. 17,428 pounds of furniture using a 28 foot insulated trailer.

The tare weight of a 28 foot insulated trailer is 8,220 pounds.

And the math for that job adds up at the weigh station at 45,231 pounds (19589 + 17428 + 8220) = 45,237 pounds (used a little fuel).

But if we reload the save, and change that same job to a triple (dry), you can see the weight jumps to 58,987 pounds. Makes sense so far.

Tare weight of a triple (dry) is 29,600 pounds.

And the math for that job doesn't even come close to adding up at the weigh station at 66,610 pounds (19589 + 58987 + 29600) = 108,176 pounds. 41,566 pounds under weight.

Swap the 58,987 pounds of cargo for the 17,428 pounds of cargo from the default job, then the math adds up (19589 + 17428 + 29600) = 66,617 pounds. So it's weighing the correct trailer, just not the correct cargo. And you can't tell me they're going to pay you 3x ($19,118 to $6,070) the price just to use a bigger trailer to haul the same amount of cargo lol. Besides, this works in reverse too. If the default job is the triple and you changed it to a 28ft trailer, your 28ft trailer is going to be hauling 58k pounds of cargo according to the scales lol.
Rest area scales give the incorrect values as well. And no it has nothing to do with the fact that it doesn't fit entirely on the scale. They weigh other long loads correctly.

(I teleported the truck around to these locations to limit fuel use and get more accurate results)