Most sheep hunts entail cutting ounces and bulk on your back. When I first started sheep and mtn goat hunting I used a scale to weigh all my gear and figure out where I could cut the most weight/bulk.
With that said, I use the cheapest, lightest disposable game bags that are available at Sportsman’s. They were a lot lighter than others and twice the length. They are super long so I can cut them in 1/2 for a boned out hind quarter.