You could by all means leave the top layer of foam mesh off and just use the cordura or xpac or what ever fabric you wanted. It would take away from some of the padding, but you could always put in a layer of foam. I have tried some with a layer of foam, and they turned out nice but add more weight, so you have to think about what you want, less weight or padding.
The weight of these are around 2.6oz for the pair, 1.3oz for each strap.
I'm not 100% sure what you mean by laying flat under weight...
I have tested them out with 25-30lbs, which is way more then I want to carry normally, in my pack and they stayed flat.