Question
A couple of days ago my weeping pussy willow's leaves began curling and dropping off.  It was just a few at first but now a majority of the leaves are curled and just waiting to fall off. I have also noticed a couple of branches turning dark brown/black from the tip inward, about 5 inches.  I would love to save this tree, it had been doing great until now.

Answer
Hi there.
Let抯 start with the easy one. Is the plant getting enough water?
Some other things are more complicated.
Bacterial Twig Blight (bacterium - Pseudomonas saliciperda): Leaves turn brown and wilt and blighted branches die back for several inches. Brown streaks can be seen in sections of the wood. Bacterium overwinters in the cankers, so young leaves are infected as soon as they unfold. The damage can be confused with frost injury. Prune out infected twigs and spray in early spring with an approved fixed copper fungicide

Cytospora Canker (fungus - Cytospora sp.): Affects willows the same as poplars. Discolored, sunken, often sharply defined areas develop on twigs, branches or trunk. Cankers enlarge and gradually girdle infected parts causing death to portions beyond. Weeping willow is susceptible, but rarely occurs on black willow. Prune out and destroy dead and cankered parts. Spray with an approved fixed copper fungicide.
I don't know where you are from but some areas also have this problem:
Cotton Root Rot (fungus - Phymatotrichum omnivorum): This disease is also known as Phymatotrichum root rot, Texas root rot and Ozonium root rot. It is caused by one of the most destructive fungal plant disease organisms that can attack more than 2,000 species of plants.
Most willow species are highly susceptible. Plants suddenly wilt and die, leaves usually hanging on the plant. Roots will be decayed with the bark peeling off very easily.
You may need to have an arborist come and look at them.