Get the Cat Scale apps. There's one to find the scales and one to use them. If you set the latter up beforehand (including giving it your credit card info) you can just fire it up, enter a code and drive right onto the scale.
If you look at their web page they have several different ways to weigh, but the most common for RVers would be just front and rear on motorhomes and front/rear and trailer on towables. $12 and when you're done they will email you a document giving you your weights (and you can also write them down). A re-weigh if you need to change something costs something less.
As David_Laura mentions, some Washington scales are left open, but more and more of those are being torn down. Also, it would take probably at least three measurements to get the same information.