Although cherries from a weeping cherry tree are not considered to be poisonous by any means, they usually do not taste very sweet like you would expect other cherries to taste. Instead cherries from a weeping cherry tree typically taste very tart and are very hard. These cherries are for the most part considered to be purely decorative or ornamental.
Some people however decide to eat cherries from these trees because they enjoy the taste though most people do not because of how bitter they tend to be. In general though most people who eat these cherries do not experience any adverse reactions whatsoever.