Weeping cherry has dead branches
Without more detailed information and photos, we cannot say for sure what the problem it.
However, some thoughts:
We cannot see the flare at the bottom of these trees. The tree trunk should not go straight into the ground (like a lollipop) but where the trunk widens out at the bottom should be above ground. Planting too deeply can kill a tree.
Also, mulch should not touch the trunk. Pull it back a few inches. Keep it no more than 3-4" deep.
Prune out the dead branches. The trees may simply have not established and been hit hard by the severe winter we just had. Many trees were injured by winter temperatures this year.
Do not drown the trees by over watering, but do supplement rainfall during dry periods spring through fall for at least 2 years as they establish. (Plants going into winter in dry soil is a big killer.)
These are not natural trees, and often are targeted by peach tree borers.
Read through this fact sheet about problems that can impact trees: http://extension.umd.edu/sites/extension.umd.edu/files/_docs/programs/hgic/HGIC_Pubs/Landscape/HG201... Drowning in clay soil planting holes is a very real possibility this year.
Send us photos if you see new or specific symptoms/signs.