The symptoms look like a type of canker disease, though we can't determine which exact pathogen is responsible. (Given its prevalence, though, it might be the disease called "willow blight.") Willows as a group tend to be vulnerable to several pests and diseases, and some infections can kill twigs or even entire branches. All that can be done at this point is to prune off areas with infection (where the twigs are discolored and shriveled, as in the photos) and dispose of the clippings (don't compost them). Keep the tree's stress low by monitoring it for watering needs during this ongoing drought. There is no effective or practical treatment using fungicide, nor would such chemicals be able to cure existing disease. Due to chronic stress from high heat and the nature of the plant, weeping willow tends not to be a very long-lived plant (perhaps 20-30 years or so). If the tree reaches the point in the future where it's too large to manage canker removal and has declined enough to be an eyesore, you may want to consider replacing it with a different species. (To be fair, all trees have their own vulnerabilities to certain pests or diseases, but willows are prone to more issues overall than most trees.)

Miri

You're welcome.