Hi, 

This looks like sooty mold growth. We can see some Spotted Lanternflies on the trunk and they are most likely feeding on the tree sap and then excreting a substance that is referred to as honeydew. There could also be a scale insect on the tree that is a common pest to Willows but we can't see the bark closely enough. 

Regardless though, if the tree appears to be dying it is most likely from other causes. Willows are not long lived and have a variety of issues that effect their health. 

We wouldn't recommend trying to treat the Lanternflies as they are so abundant now and doing so would be harmful to beneficial insects. They are mostly considered a nuisance pest and their populations have shown to decline after they spike. They won't be the main cause of tree decline to the willow.  

If the limbs are breaking and dropping, you should contact a licensed tree expert or certified arborist to evaluate the tree and help prune any potential dangerous branches.

Emily