OR and WA are both 10,000# states for tire chains. Under 10k may use studded or snow-rated stud-less tires.
The 6,000# rule only applies to conditional road closures, where chains are required for everybody. Unless you are under 6,000 pounds with snow tires and 4x4 engaged. This rarely happens anymore, because by the time the roads are bad enough traction tires won't get you up it, there's already a dozen or so out-of-state semi-trucks blocking the highway.
The other issues is insurance.... vans and trucks over 10,000 pounds have to buy commercial insurance in some states, and that's probably where the RV registration helps the most.
2000 E450 dually V10 wagon