Question
globe willow has black areas on branches and some weeping of a clear substance

Answer
Sound like aphids or scale insects. Both will suck the plant juices from the leaves and twigs and secrete a substance called honeydew. Both are insects--If it is aphids you should see small insect that maybe covered with a waxy material that when you touch them they will move. The scale insects live under a shell like structure and look like a small turtle and are attached to the limbs and do not move. Both suck the plant juices and produce honeydew. Honeydew is high in sugar content and is sticky to the touch. Usually a black sooty mild will grow on the honeydew making everything black and sticky. Control the aphids or scales  and the honeydew and the sooty mold  will go away.

Both insects can be controlled with the same treatment. You can either spray the tree's foliage or use a systemic insecticide on the soil beneath and the tree will absorb the insecticide through the roots and take the insecticide to the leaves and twigs. Spraying a large tree can be difficult.


Chemical Control - Contact Insecticides Numerous contact insecticides are registered for aphid control. Since aphids are often placed under considerable pesticide pressure in field crops and greenhouses, they may be resistant to certain categories of insecticides. Therefore, if you do not obtain reasonable control, consider rotation to another insecticide. Contact insecticides currently registered for aphid control include: acephate (Orthene),  bifenthrin (Talstar), chlorpyrifos (Dursban),  diazinon,  malathion, nicotine sulfate, pyrethrum, rotenone, resmethrin, and tetramethrin + sumithrin.

Chemical Control - Systemic Insecticides Several systemic insecticides are useful in aphid control. Aphids have sucking mouthparts and are thus very susceptible to pesticides located in the plant vascular system. Some of the systemic insecticides also have contact activity. Systemics injected or applied to the ground are less harmful to beneficial insects. Systemic insecticides include: acephate (Orthene)


Certain persistent insecticides that move systemically in the plant may provide control through the fall. Imidacloprid (Bayer Advanced Garden Tree and Shrub Insect Control) is a newly available systemic insecticide that can provide aphid control on trees for several months following application to the soil. I would recommend using this product since it is easier and gives a longer control than the spray products.  Check with your local nursery/garden type store for these products.