Can I get a starter off a weeping cherry tree?

A bud is taken from the cherry tree and and grafted into a tree called the stock root tree by making a slit. After the bud growing to a certain size, it's detached from the stock root tree and planted separately. You have to wait till spring to plant a new one.

Lots of more interesting info through the source website.

All weeping cherries are grafted onto the top of another cherry, a somewhat complex process in this case because one is not just grafting onto rootstock, as is done for apples and the like, but the top of a japanese cherry that is already several feet tall. Cherries, being thin-barked and prone to infection, are also a somewhat difficult grafting subject. It also takes many years of pruning after the fact to get the desired all-around "weeping" effect desired without any shoot growth from the parent stem.

The often steep retail price of weeping cherries at the nursery is a reflection of the time and effort put into their creation (same thing with many varieties of japanese maple), so unfortunately, I would say that foir the average person, it is really not worth the time, effort, and expertise it would take to actually create one from scratch.

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