You will certainly stiffen the floor by adding another layer of plywood, but the foam insulation between the layers will not provide a good bonding surface. If I were undertaking this task, I would definitly use Liquid Nails or similar bonding agent. In order to ensure a strong bond, I would make sure I cleaned the surface of the existing flooring very good, maybe even sand it a bit to give the bond a good surface, doing that you will never be able to remove the sections you add. As far as weight is concerned, keep in mind a 4x8 sheet of plywood typically weighs 25lbs per 1/4 inch of thinkness. I would think 3/8 to 1/2 would be excellant for your application. Remember to paint the added wood, making sure to get the edges liberally with a high quality exterior paint to seal the wood. Another idea you may look into would be to adding 2"x3" joists accross the span you want to stiffen. Spaced every 12-16 inches, then cut foam board to fit between them, then seal it with paint and a thick plastic sheet for weather proofing.
2006 Nissan Xterra
B&M Trans Cooler
2011 Nomad 206
Panasonic/Pioneer/Kicker ~ Audio/Video System
Days Camped /2009 / 33