Q.A sentimental weeping willow is having trouble.
I have an old weeping willow that is having trouble. I had it pruned, but it is still dropping lots of willow branches. I had a large area decorated under the tree with rocks. The gardener used a very heavy fabric under the rocks which was fine, but I noticed after several years, that the tree was struggling. I had the fabric cut back about 10 ft. and found a lot of dead roots and soil depletion around the dead root areas. We took out dead roots,replaced the missing soil with good soil, and put more river rock down sans fabric. The tree seemed better after we did that mid to late summer last year so I am surprised it is still dropping lots of dead willow branches. Oh, and I also watered and fertilized it last year as well. What else can I do?

A weeping willow is relatively short-lived compared to some trees. The maximum average lifespan is 50 years, and they may began declining as they age.
Depending on the age of your tree; you may be seeing just normal signs that the tree is coming to the end of its life expectancy.
https://www.gardeningknowhow.com/ornamental/trees/willow/planting-weeping-willow-trees.htm