I have a weeping cherry that had dead limbs on one side because of a larger tree. We cut back the larger tree and the dead branches off the cherry. Now the cherry is very lop-sided, weeping to the right and nothing to the left. Can some of the growth from the right be cut and grafted into the left? If so how?
I think if you are willing to give it a few years the tree will grow and fill out the barren side. Even if you graft some of the branches from the full side it will take time to fill in. When you do the winter pruning on the tree, don't cut much in the area you want to fill out. If you were thinking of possibly grafting large branches to fill in the empty spot instantly, I am not too sure about that. I have not done grafting, but I think it is most successful on smaller newer growth. Grafting is probably not the easiest project for a novice. I could be wrong, maybe a more experienced tree fruit grower has other ideas for you. Good luck,