Hey there!
A couple things to check on your meshes before exporting them to fbx. First, make sure your history is nice and clean. You should have the skinCluster node at the top of the history stack. If not, things go bad.
This:
Not something like This:
If you have history like above, you can try doing delete non-deformer history on the mesh, and try exporting again.
Also, if for some reason that wasn’t it, check to make sure your meshes don’t have a crazy number of UV sets. I think fbx supports up to 4 UV channels. Sometimes, I’ve seen meshes that come into Maya with tons of channels.