Answer: Based on your description, unfortunately I am not able to think of a weeping tree that would work for you. Most weeping trees are wider than they are tall. The closest I can think of to the size you want is Malus x Louisa at about 15 by 15 feet, too short. And if the site was too wet for a cherry, I am not sure a crabapple will do any better. Perhaps you could work with a landscape architect to devise a way to drain the area better (a wet corner is not all that good for a foundation) and then plant the cherry.
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