I prefer to make my quivers of about 6 oz. leather, which is a compromise in softness and thickness. However, to supple up the leather, you must work it around in your hands, rolling and unrolling the leather, while using some type of leather oil. You can have quite heavy leather be soft enough to fit you your back this way. I also always put a double thickness leather bottom, about 1/4" thick, with carpeting to make it quiet.
I don't like a quiver that's so soft that it collapses when I bump the bottom up to reach an arrow.