Question
I HAVE GREEN MOSS AND WHITISH GREEN STUFF GROWING ON THE BRANCHES ON MY WEEPRIN CHERRY TREE?

Answer
These sound like lichens. Lichens are an example of a symbiotic relationship between algae and certain fungi. They are capable of producing their own food. The algae associated with the fungus is a green or blue-green alga. There are three forms of lichens based on growth patterns. Crustose are species that are closely pressed against the surface of the limb or trunk of dead or live trees. Foliose forms are leaf like or prostrate but are also tightly attached to the tree. Fruticose forms are bush like, erect or hanging. Although lichens are found in most areas of Texas, they are most noticeable in areas that have extended periods of high humidity.

The effect of lichens on a tree are only slightly detrimental. The plants are epiphytes. That is they derive their nutrients from the air and not from the plant on which they are growing. Although they are not parasitized, literature reports suggest that lichens do have a slight negative effect. The main concern is that lichens give a tree an unkept appearance. Presence of lichens also is a good indicator of a thin tree canopy. This often leads homeowners to conclude that lichens are the cause and not the effect of thin foliage. The best control for lichens is maintain the tree in good condition. This will insure a dense canopy which will shade the limbs and reduce photosynthesis. Without photosynthesis, lichens are not able to manufacture food needed for growth and development.  

Fertilize the tree with  10-10-10 fertilizer at the rate of 1 lb per inch of trunk diameter scattered around the tree and watered in good. Apply just before a rain storm and you will not need to water it in.