Look at the tree after planting it. Locate its center-most trunk. Retain that stem, and remove all others at the soil line with loppers or a pruning saw. This step is optional and solely based on your preferred form for the plant.
Find the bud union on the tree to confirm the plant is grafted, usually the case with weeping pea tree varieties. The union is a bulging area below the crown where the nursery propagated the tree using a rootstock. Prune any branches that begin to develop upright on a grafted weeping specimen. The standard rootstock used produces those twigs. They never droop downward. Remove them at the point where they originate. On naturally weeping plants, erect stems arch after they gain some height.
Trim branches that reach the ground, if that is your preference. Otherwise, let them drag. Cut into the wood at a 45-degree angle, 1/4 inch from a bud.
Remove crossing, dead, and diseased stems at their point of origin on the tree. You can see what is going on with the branches more easily in the dormant season when the plant has no leaves.
Thin the pea tree's top branches to 2 inches apart. This space allows adequate air circulation within the plant. Prune any twigs that sprout below the crown.