Weeping willow disease?
Your willow is suffering from a disease called crown gall. Crown gall is caused by the soil bacteria Agrobacterium tumefaciens, which can survive without a host for two years and significantly longer in decomposing galls. This bacteria also survives on seeds, making it difficult to eradicate in an infected area. A. tumefaciens do not enter healthy root tissues, but when roots or trunks are damaged during planting (or by the activities of soil insects and nematodes), infection occurs rapidly. Pruning tools also transmit the bacteria to stems and branches.
Crown gall swellings may resemble scars left by grafting unions or deep wounds on willow trunks, but they grow much more rapidly and can appear anywhere on the tree. Developing crown galls are often white or light-colored, round and soft. They grow irregularly as they harden into a woody mass with a corky surface. These galls, up to about 50 pounds and a foot in diameter, eventually begin to rot and fall off in pieces. New galls form in the same location, or nearby, on the tree. Large galls may girdle young trees, interrupting water and nutrient flow and ultimately causing their death.
On older trees, like yours, remove galls by cutting all around the gall and into the healthy wood by about an inch when the weather is dry. Prune out affected branches and dispose the diseased wood in the trash. Take care to disinfect your pruning tools by wiping the blades down with 70% wood alcohol so that you do not spread the disease to other parts of the tree or to other plants.
Willows are beautiful, fast-growing trees but they are very susceptible to a number of diseases and are not long lived. If you are really attached to the tree, you should consider having it evaluated by a certified arborist for evaluation and treatment.