About $5 a mile + all the expenses of having the car itself.

So, they don't consider weight?

If your private car is "that" heavy, and they need to hook up an extra locomotive just for you, then that is going to be a steep fee per mile added.

They actually mention it in the PDF under "more locomotives" or something.

I think that mainly applies when you add a whole train to the train (you can hire them for multiple private cars)

It's a passenger car, it weights basically nothing compared to a coal car so they probably just assume "some default" weight.