I've struggled so much to figure out why my dragon mesh moves with the armature, except the wings, which just get stuck in place and don't move with the rest of the mesh (it's all as one object and parented). Although, I'm not sure that the object and armature have been parented corrected with weights. Below is the link to my blender file. I really need help with this and anything would be appreciated :)
You should unclick the Bone Envelopes option of the Armature modifier of the mesh, then select the armature, shift select the mesh, ctrl tab to switch to Weight Paint mode, then select each bone and paint the mesh accordingly to the influence you want this bone to have on the mesh.
Or even delete the Armature modifier and reparent the mesh to the armature With Automatic Weight and then bring some corrections in Weight Paint mode...