I line the inside of my outer covers with 2x4's or 2x6's and make the rims taller... I put... 1/4" strips between the 2x's and the actual cover to create an airspace for ...insulation...
I was thinking, why not use 2X4s or 2X6s for the lid frame, add a 3/4 inch plywood cover and a second cover over that made out of 1/4 inch corrugated plastic political signs, then add a crimped metal top over it all. If weight is what you want this lid should be plenty heavy enough and the corrugated plastic sign will provide the added insulation you are seeking.