The question is very general.
If a 1.5mm and a 2mm sponge is made of the same material the 2mm sponge will be softer.
It is the air bubbles that make sponges springy. I doubt it makes much difference on the size of the air bubble. i think what is important is the ratio of air bubble to actual sponge. The air bubbles are very good at returning absorbed energy. The trick to making sponge is to keep the air bubbles the same size and uniform throughout the sponge.
For best spin the sponge must be soft enough to let the top sheet stretch across the surface. It is the top sheet snapping back that provides extra spin.
Ignore words like tension. I have yet to see any formulas having to do with the spin or speed of a ball that affect tension. The COR or coefficient of restitution is what is important but TT manufacturers don't rate their rubbers that way because it would expose the awful truth.