A small tree native to Japan, weeping cherry trees (Prunus subhirtella) grow in U.S. Department of Agriculture plant hardiness zones 5 through 8. They grow up to 40 feet tall and wide, but many varieties stay under 20 feet. Although not difficult to care for, weeping cherries have some specific needs that you must meet to get the most out of the tree.
Water the tree -- up to 84 gallons of water -- once per week during dry periods. While weeping cherry trees don't perform well in wet conditions, they need water to grow and bloom properly, especially in sandy soils.
Spread a balanced, acidic fertilizer starting 6 inches away from the weeping cherry tree trunk. Broadcast the fertilizer to just beyond the drip line in spring, when buds form.
Prune the weeping cherry right after it flowers in the spring. Remove water sprouts, or limbs that grow upright, and any dead limbs. Trim any branches that touch the ground. Make cuts at a 45 degree angle, about 1/4 inch away from buds. Thin out branches that rub against one another.