I'd be inclined to use marine grade plywood, and coat it in a outdoor grade sealant or epoxy. I put marine ply in my boat and has been left wet for extended periods and is holding up just fine. Should be lighter than manufactured wood or plastic as well.
I'm not sure the climate you are in, but I'd also put a large desiccant inside to avoid internal humidity from building up too much. That could be as simple as a sack of kitty litter.