I'll admit to using kind of flimsy cardstock for my layers - the Recollections brand assortments at Michaels, or the Coredinations assortments at Joann's, for example, for my layers - it doesn't add quite as much weight. I even bought a ream of black text-weight paper on clearance at Office Max once, and I use that for layers because it adds almost no weight or bulk. I just make sure the base of the card is good and sturdy.
Any time you add a layer or embellishment, you're going to add weight, and that's ok. It's a handmade bit of art, you don't want it to feel disposable