I've haven't seen any sites reservable in recreation.gov or reserveamerica.com that did NOT list size of RV usage for each site.
National Park and National Forest parks usually will tell you about the sites on their web sites.
In North Carolina here's an example of Forest Service campgrounds LINK
Also in NC National Parks.LINK
By going to this site
you can find all the National Parks and information about them.
covers all the National Forests.
I hope this helps a bit.