Timing for Tree Trimming
The rule of thumb is to prune spring blooming trees and shrubs just after they bloom. This explains how to prune in general: http://extension.umd.edu/sites/extension.umd.edu/files/_docs/programs/hgic/HGIC_Pubs/TreesandShrubs/...
However, Weeping cherries, do not require regular pruning except to remove dead branches or branches that rub each other and may cause wounds. Extensive pruning would ruin their graceful form. A wide mulched area or bed of groundcover beneath it can make it unnecessary to prune up the lowest branches for mowing and thus preserve its beautiful branches.