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Yeah, I realized that after we watered the lawn, and it did start to bow alittle. We were using some old paint(matched our house) that was left in our garage after our house was built but we ran out. I was planning some tar paper and maybe put a pitch in it?
A pitched roof would likely be best, have to be a little careful with how it runs off since it is right up to your house. If you wanted to leave it flat you could get a rubber membrane to go over it, but they are a bit costly. Depending on how you design it, you may need to use some flashing up against the house to protect your siding. Remember normal shingles are not for a flat roof and will end up leaking. I had just mentioned the 2x4 and paint solution because it would end up making it last for a while for say $30, A pitched roof with shingles or metal panels will last for decades, but the cost is much higher.
If you use 2x4's to help hold the plywood flat, you can use construction adhesive, like PL400 to poly adhesive to glue the 2x4 to the plywood, that will help the plywood keep it's shape longer.
Jamie