Although a number of ways exist for propagating a weeping cherry tree, grafting is a good way to ensure the propagated tree has the same genetic characteristics as the parent tree. Although grafting is not difficult, it may take a couple of attempts to get right. Once you get the hang of it, however, grafting is a very easy and reliable method of tree propagation, especially for weeping cherries.
Gather scion wood (twig or stem that produces a leaf or flower) in the winter when the main tree is dormant. With sharp pruning shears, cut approximately pencil-width scions 8 to 18 inches long from the previous year's growth.
Put the scions in plastic bags with damp peat moss. Place the bags in the refrigerator until you are ready to graft.
Watch for the buds to swell on the ends of existing outdoor trees. Swelling outdoor tree buds means the proper time for grafting has arrived.
Make a diagonal cut on the main trunk of your root stock from one side to the other. Make this cut between 1 and 2 inches long. In the middle of the cut, use your grafting knife to cut downward through the center of the trunk to the bottom of the initial cut.
Make a matching cut on the bottom of the scion.
Slip the tongue of the scion into the tongue of the root stock and wrap the union securely with masking tape.
Cover the union and tape with grafting compound or grafting wax to seal the graft. Remove the compound and tape as soon as the scion starts to grow.