I have always maintained that balance and feel are every bit as important as is weight; even when just carrying.
I generally carry the rifle in my hand when I am packing in and I really want it to fit comfortably in my hand and balance well. Weight isn't super critical but there are some limitations, of course.
I have an old Model 70 which I have always liked (a 308 Norma) but it weighs close to ten pounds, all up. After a few miles my old, arthritic hands have had all they want. As long as the rifle is under eight pounds though, I'm still OK. When an eight pound rifle becomes too much, I should probably quit the whole backpack thing.
Please understand, I'm not saying a person shouldn't go for a lightweight rifle; saving weight everywhere just makes sense. I have just never been so inclined; mostly because I already have all these old-timey rifles which weigh a bit. I also still carry a two burner stove on my back! GD