Obtain a mulberry sapling from a commercial nursery to ensure it is a weeping variety. This typically consists of a weeping mulberry scion grafted to normal rootstock, and is generally one to two years of age. A weeping mulberry tree is a hybrid that may not grow true from seed.
Fill the largest available container halfway full with rich loam. Cut the nursery container down the sides with pruning shears, allowing you to remove the weeping mulberry tree from the container without disturbing its roots.
Place the weeping mulberry tree in the container and spread out its roots as much as possible. Fill the container with additional soil until the soil rises to the level of the tree's soil line.
Put the weeping mulberry tree in full sun for the best growth, such as a southern window. This tree can also tolerate partial shade.
Water the tree with 1 to 2 inches of water per week to keep the soil moist. Ensure the soil drains completely before watering a weeping mulberry tree.
Prune a weeping mulberry during the fall or winter after the tree drops its foliage. This prevent sap from seeping out of the cut, which can weaken the tree. Remove any diseased or dead growth, and trim the tree to the desired shape.