The Weeping Mulberry "Pendula" is a dwarf, weeping mulberry cultivar that typically grows to only 6-10’ tall. It is usually top-grafted to a larger species tree, with its gnarled branches weeping to the ground.
The variety "Chaparral" is the non-fruiting male version.
The Weeping Mulberry is definitely an oddity in the garden, interesting and different. The ones we have seen growing in Southern New Mexico seem to be healthy and doing well in the desert heat.
See the Fruitless Mulberry for more info.