Weeping cherry trees are beautiful trees that provide lush green vegetation in the summer, pretty flowers in the spring and colorful leaves in the fall. Having one of these trees in your landscaping gives the space a focal point, but you must be vigilant about protecting them from diseases and hungry insects.
Aphids are an issue for many types of trees including the weeping cherry tree. Aphids eat the leaves and deposit a sticky substance on the tree. This "honeydew" attracts ants. The aphids usually leave by the middle of summer, but the damage is done for the year. If you notice the stickiness and ants in time, a basic insecticide can be sprayed to remove the problem.
Japanese beetles come in droves and will eat holes in your tree leaves. Getting rid of these bugs is a chore and usually requires a stronger pesticide such as Sevin Dust to keep them off of the leaves. Apply liberally on the tree, making sure to coat the undersides as well as the tops of leaves and reapply when it washes off. Japanese beetles start out as grubs, most likely in your yard, so if you treat the yard before they fully develop, you can avoid the issue.
Bag worms are prevalent in cherry trees of all types including weeping cherries. These are the most obvious to see and remove before they do damage if you pay attention. They hatch in a webbing that protects them for a while. When they break free of the webbing, they start to eat the leaves, leaving holes behind. You can use a tree trimmer to cut the bags out of the tree before they get loose.
There isn't much you can do to keep weeping cherries free of all bugs, but there are a few things you can do to help. Trim tree limbs when they start to get long and droop to the ground. This will keep bugs from marching right up the limb. Water the tree when needed to help keep it healthy, and prune out dead or crossing limbs as well.