If I were looking to build as light of a rifle as possible and still have legit consistant 500 yard reach, I would probably go with a 280 AI. The reason would mainly be that the 7mm offers a great selection of bullets. My first choices would be the 169.5 gr ULD RBBT Wildcat or the 160 gr Accubond.
These are more then you need for sheep but in sheep country it is often windy. Alot of times VERY windy with alot of updrafts, down drafts and multidirectional winds. The high BC bullets would help greatly in these conditions yet still they are not so heavy that recoil would be severe.
The 280 AI can be housed in a Rem 700 which is lighter then most custom receivers of the same design. I would go with a carbon fiber Manner stock, two piece Burris DD bases and DD signature rings with a lightweight Leupold scope in the saddles.
More then likely I would use a DE brake as well. barrel length would be 24" and barrel contour in the #2 to #3 Lilja range, 1-9 twist 6 groove.
The 280 AI will do pretty much anything the 7mm WSM
will do and feed MUCH better as well then the stubby fat WSM. Most of the 280AIs I have built for customers come suprisingly close to matching the 7mm Rem Mag in 24" barrels.
For a bit more weight though, I would also lean toward the same basic rifle but with a 26" barrel in 270 AM loaded with the 169.5 gr ULD RBBT to 3350 fps. 500 yards would be a chip shot and terminal energy would be far greater then most other chamberings in such a light weight rifle.