uh, being a commercial vehicle has nothing to do with weigh stations. Granted, the chances of you getting pulled over for not stopping in a u-haul are slim.. but..

It's ENTIRELY UP TO THE STATE what has to stop. Minnesota, the 3 axle rule is there as well, but in wisconsin (I think), and south dakota I ensure you it's not.
Just check the GVW (Gross Vehicle Wieght) plate (usually on the doorframe on the drivers side door), and stop for anything that says "All Vehicles over X GVW must stop". I drive a truck that I have to stop in South Dakota (6,000lb GVW for whatever stupid reason), and they just wave me through without even wieghing. (truck is 15,000lb GVW).
So your answer is, you probably will be fine if you don't stop. But if a cop wanted to be a jerk...
and, don't take the u-haul guys' word for anything. Do what I said, otherwise you may be trusting a ticket for not stopped to some high school kid who never drove the thing anyways.
-Phil