Do you know what kind of tree this is? From your picture, it's possibly either a weeping cherry or a weeping plum tree. The plum would have purple leaves.

These weeping trees have a life expectancy of around 15- 20 years, though they can live longer with proper care. They also are susceptible to pests and diseases. Additional information about the tree would be needed to determine what is happening to your tree.

For example, have you seen any insects on the tree or leaves? Any spots or webbing on the foliage? Is the tree in good soil? Was it properly planted? Do you keep it fed and watered? etc.

I suspect the tree is nearing the end of its useful life. If this tree is valuable to you, your best resource for diagnosing and treating it is to consult a certified arborist. An arborist is a certified and generally insured expert in trees and their problems. He or she can examine your tree and make recommendations regarding the health of the tree, any needed judicial pruning, and whether or not (in his opinion) it should be removed. You can find a certified arborist in your area here:

http://www.treesaregood.org/

Click on "Find an Arborist" at the top of the page; then click on United States from the pull-down menu. Then enter your State and City. This should bring up a list of certified arborists nearest to you. Or you may be able to locate one under "Tree Services" in your local Yellow Pages.