Coroplast is light, tough, and probably weatherproof, but it isn't cheap, at least not in new 4'x8' sheets.
If you can find it as scrap in the size you want, you might get it free or cheap, but for target backers I'd think you'd want fairly large pieces.
On a related note, most shooters overbuild their target frames, especially ones intended to be portable. I see guys manhandling frames built of steel and 2x4s. For years I've made mine from furring strips with cardboard stapled on, and they've held up even in the wind. Easily repairable and replaceable too.
Paul
