Instead of piling your fabrics on top of each other, try some flatter bins, and then set your fabrics in on their sides.
I have large plastic bins about 8" deep, and fold the fabric to fit. When I open the bin, I can see the panorama of colours as a quick view. My stash has grown now, so that my soon-to-be next step is to sort by colours with a separate sections/bins for florals, Christmas & seasnals, novelty prints etc.
I have now started to leave the measurements with any pieces that are a metre or larger in size.