Answer: You might be able to grow one of the taller, woody PeeGee type hydrangeas (Hydrangea paniculata) in that location; when trained to a tree form they weep somewhat when they bloom because the flowers are so heavy. And, they can reach the size of a small tree. Angel's Blush for instance grows to about 8 to 12 feet tall and up to 10 feet wide. Hydrangea paniculata 'Grandiflora' is a bit larger at 10 to 15 feet tall and wide.
Most of the usual weeping trees such as weeping crab apple or weeping cherry would require a full day of sun or at least six hours of sun including the hour of noon to stay healthy. Unfortunately I can't think of any weeping tree that will tolerate shade.
Your local professionally trained nurseryman may have other suggestions based on a more detailed understanding of the growing conditions in the spot where you want to plant and your overall design goals. Good luck with your project!
Q&A Library Searching Tips