Answer: I, too, have a weeping cherry with some branches that want to grow straight out rather than hanging down. I guess it's just the nature of the beast. I wait until the tree is dormant (late winter) and then prune out the offending branches. Since pruning encourages new growth, be sure to wait until very late winter or very early spring before pruning or you'll end up with new growth that is not winter hardy. Other than pruning these errant branches out, you might be able to coax them into hanging downward by attaching a stone to a piece of string or twine and attaching it to the branch. The weight of the stone should train the branch into a downward growth habit.
Best wishes with your weeping cherry tree!
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