J, I have an A7 from when they first came out about 6-7 years ago. It had the hard plastic tupperware stock.
Couple years ago I replaced the factory stock with an EDGE.
The EDGE stock is actually a couple ounces heavier than the factory stock. It's a little wider and just a more solid stock.
If you have more recent vintage A7 the stock might be different and you could actually save weight but I'm just guessing.
I obviously didn't shave any weight but did end up with a rifle that is nicer to shoot. The EDGE stock soaks up recoil better than the plastic and that alone is worth it.
Zero gain in accuracy, a slightly heavier stock but a noticeable reduction in felt recoil. Mine is a 300 WSM that weighs about 7.5lbs scoped.
And FWIW, if you want to replace the factory A7 shroud with a nicer stainless/blued version the Sako 85 shroud will fit.
http://www.brownells.com/search/index.htm?k=sako+85+shroud&ksubmit=y 
