I recently bought a g305 and was wondering how I could cut the weight even further with a lighter battery than the one you get with the mouse even anyone had any recommendations that would be really helpful.
AA batteries are all going to be around the same weight. Any differences between single batteries are going to be so positively minuscule that you won't notice a difference. If you're really committed though, you can go to a site like Amazon and compare product shipping weights against each other.
Look for something like this. Keep in mind it's going to include packaging weight too.