Err, no need to stay out of state weigh stations if they are closed, or if they aren't busy. Yes, there are some states that frown on you using the scales if they are busy, and I don't. But most will readily accommodate you. You see, it's a SAFETY issue and no one in their right mind is going to hassle you about trying to be safe with a 20,000-40,000 pound vehicle by getting it weighed.
Couple ways to do it.
When closed, just drive in and weigh your right front, the scale displays are put where you can see them and nearly always left on, write that down, move the right rears onto the scale, write that down, now circle around (or just back up if you can) and do it again so you weigh your front axle, than rear axle. Later you can do the math so you have a four corner weigh. (Not all weigh stations are built to accommodate 4 corner weighing).
When open, but not crowded. Park somewhere, walk over and ask if it's ok if you weigh. 90% of the time they'll say fine. Just do the front axle, than the rear. Don't attempt the 4 corner weigh. If the place is open but empty, just drive right up to and onto the scales, the guys will just wave at you. Write down your weights and off you go.
I often see RV'ers weighing their rigs on weekends when most of the state weigh stations are closed. But I travel during the week mostly so I'll usually look for that occasional 'closed' station rather than the open ones.