Weeping Atlas Cedars often suffer from aphid so my best guess is your tree is showing damage from aphid that attacked in early spring. By early summer the aphid have matured and left so you won't see any at this time. Perhaps you can bring a sample to a local arborist to confirm the aphid attack. You can use a dormant oil spray or a strong jet of water in early spring to dislodge the aphid. Just bombard the branches with a strong jet of water every few days to dislodge the pest. Meanwhile you should cut off the brown branches to tidy up the tree. Keep growing, Marianne Binetti