Dig a hole with the shovel three times the width and 1-1/2 times as deep as the rootball. Add 4 cups of tree fertilizer to the hole. Do not remove the burlap, which will degrade and provide food for the weeping willow tree.
Fill the hole with dirt, keeping the tree as horizontal as possible. Add a handful of fertilizer for every 8 inches of dirt.
Cover the last section of the weeping willow tree and pack the dirt down gently. Water the tree for about 15 minutes with a garden hose.
Water the tree at least daily for the next month with a garden hose for about five minutes. Add more soil if it seems to be giving way. Do not water on days that receive 1/4 inch or more of rainfall.
Spray the tree with insecticide after it has been established, typically after the first 30 days, to help remove potential pest problems and keep the mosquito population in the tree down. Mosquitoes love living in weeping willows. Follow the insecticide's label instructions for dosage amounts.
Prune the branches that are too long or not pleasing to the eye. Re-apply the insecticide each spring, as often as twice a year, if necessary. Remove dead branches in the spring.