Depends.
Some states say yes, some say no. Illinois, for example, requires a GVWR of 8 ton to enter the scales. Iowa and Wisconsin require 6000 pound GVWR vehicles to scale. Other states, like Virginia require all commercial vehicles to scale; however these states define commercial vehicles differently. 10,001 pounds for some states and 26,001 for others, like Missouri. Some states use registered weight and others use GVWR.
I have always driven a van and when we started we entered a scale in every state we travelled. Some scalemasters told us to stay off their scales but most politely said we needn't enter. A Canada Scalemaster said we did not have to enter but that it would be 'nice' if we did, on occasion.
To this day I have never seen a definitive answer to your question, so, it depends. Perhaps someone has the answer to satisfy all of us in the questionable area of weight and size.
Terry