This little weeping tree is in the front yard of our new house. We just moved in this month and have observed no flowers or fruits. It has a single woody trunk, some kind of buds are forming at each leaf node, and the leaves are quite leathery. It's about 6' tall. It's been hot here and nothing has been watered while the place was empty, everything is stressed. In the back yard are plums, Asian pears and a variety of beautiful plants, so I imagine this is something special, but what? Anyone recognize it? The cats love to hide under it.
I believe you are right, I googled a bunch of photos of weeping pussy willow and got lots of photos that look just like our little tree. Yes, I think Salix caprea 'Pendulata' is probably exactly it! I'll post photos of it in early spring. Thanks to you both!