3/4 ply gets really heavy, really quickly. Try to find 1/2", usually labelled as 7/16". It's much lighter. And if your footprint is only 4x4, you won't need that much material, it won't be that big of a cost increase.
If you get any rain in your area, don't use plain ply. You will need to cover the plywood with some kind of siding or tar paper(which will only last a few months). Moisture gets into the wood and causes it to delaminate and warp rather quickly. Even if you paint it. OSB is even worse, and most people mistakenly call OSB plywood, so be careful of that.
A far better solution is to build the frame with 2x2s, and then cover with cedar siding. I know cedar siding looks expensive, but with such a small coop it wont cost that much. It stands up to all kinds of weather, and it looks nicer.
