I also have a weeping cherry, and the branches are also resting on the ground. I found this website looking for answers to the same questions. Also, my tree's trunk has been "sculpted" so that it twists, and the trunk, unlike many weeping cherry trees, is the actual cherry tree, not a host tree for propagated (right word?) cherry branches. I'm not sure if I need to do anything to it -- just let it go, or try to keep it twisting/curving?