The thickness of the backing can be relative but I don't know that I would ever want to use thick backing because then you'll have "bullet proof" embroidery. You may need to lessen your stitch count.
Bullet proof embroidery is more a product of stitch density, rather than backing.
Although, if you put 4 or 5 layers of heavy cutaway behind a shirt it will be quite thick and firm, but after a few washes it will start to soften up (but still be thick)
Most backings will soften a bit each time they are washed.
For sports fabrics, I have two ways of backing the material..just depends on the fabric.
I use either 2 layers of cutaway with a layer of solvy on top or 1 layer cutaway and 1 layer tearaway on back with layer of solvy on top.
However, if you can find the mesh backing, I would use that, it appears to be working for that material.