Is there a way to see how the storage size of each layer in Illustrator, InDesign or any of the Creative Cloud?
None of these programs will give you the file size of individual layers because the 'size' will depend on the format that you save the file in. If you need to know how big each layer is in your desired file format then your only option would be to save each layer as a separate file. i.e. by deleting all the other layers and saving out each layer individually.