Although you can sometimes grow weeping cherry trees from seed, grafting a scion to a compatible root stock assures that the propagated tree will have similar characteristics to the donor tree. Grafting is not difficult, but might take a couple of attempts if you don't have much grafting experience. In most cases, you will have more success by selecting a root stock with a trunk about the same size as the scion you will attach. Whip grafts offer more contact area in the graft and sometimes work better than other types of grafts.
Make a 1 1/2- to 2-inch angled cut from one side of your root stocks trunk to the other. This angled cut will form the main part of the grafting area on your root stock.
Make a cut through the center of the grafting area. Begin halfway through the angled cut and continue downward to the start of the angled cut. Cut, do not split, the wood.
Make an identical angled cut on the scion. If you made a 1 1/2-inch cut on the root stock, make a 1 1/2-inch angled cut on the scion.
Make a center cut on the scion like you made on the root stock.
Slip the scion into the root stock, mating the central tongues. The inner bark of the root stock and scion must make contact on at least one side.
Wrap the graft tightly with masking tape to hold the graft together securely.
Cover the graft and tape with grafting compound to seal the wounds for the time it takes for the graft to heal.
Remove the grafting compound and tape as soon as the scion begins to grow to avoid having the tape and compound grow into the weeping cherry's trunk.