I think Ted has nailed it. It will be impossible to perfectly align the warp/weft (horizontal and vertical threads) of the two fabrics when you fuse them. From that point on, one piece of fabric will be fighting what you try to do with the other piece. Fold a perfect pleat on the outer half, and you will be folding across several vertical threads of the inner half. Plus the difference in radius that Ted mentions.

You can get more "heft" from a lighter weight fabric by making the pleats deeper (i.e. put more fabric into the fold) and doubling the apron without fusing the two layers. This isn't the best solution but if you can't find the weight of fabric you want, it's one way to compensate.