What are the damages, if any, to ground cover under a weeping cherry tree? I have been told that ground becomes high in negative nutrients. Care to comment, please.
I believe you are referring to the chemical Juglone, which is given off by the roots of certain trees. Black Walnut is one of the worst alleopathy culprits.
Black Cherry Tree is listed as alleophatic, but you do not need to worry about a Weeping Cherry Tree.
Here are some articles with more information.