Answer: Generally the weeping cherry (Prunus subhirtella cv. Pendula) is a naturally pendulous tree. Sometimes weeping trees are created by grafting a weeping-type top onto a standard trunk. That sounds like your situation. If so, it's important to prune out any branches that sprout below the graft, so these non-weeping branches don't overtake the top part.
Have you done any pruning in the past? If you prune back the weeping branches, this can cause the branches to stiffen and become more upright. Also, any heavy pruning can stimulate the tree to produce vigorous upright shoots called suckers. Prune weeping trees with a light hand, removing crowded and crossing branches and any damaged wood. They shouldn't need much other pruning, and should develop a natural weeping shape on their own.
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