Not so much the weight of the F135 as the size which is too big for any of the present COD and has to be split into modules. Even then the power module in its factory engine shipping system is too big and can only be carried as an underslung for a couple of hundred miles.
One of the drivers in buying V-22 for COD is that they have had a purpose designed sled which the module fits onto and, just, fits inside the hold.
http://navalaviationnews.navylive.do...s-golden-mile/