I've used both fusible and non fusible light weight interfacing in numerous quilts for several years mainly for scrappy string quilts. The original instructions for my first string quilt used muslin as the foundation but I found that it made the finished quilt too heavy. The light weight interfacing added little overall additional weight and didn't change the hand of the finished blocks in any great degree.
I just finished remaking a heavily, much loved, ten year old hand appliqued Overall Sam quilt for one of my grandsons. Since I wanted to preserve the original blocks, I fused the back of each with the light weight fusible interfacing to strengthen them. Although, the quilt will be retired from daily use, packed away as a keepsake or used as a wall hanging, other than having to replace the original sashing, borders and binding, it is otherwise original. My, now sixteen year old grandson, was due for a quilt more age appropriate, which I'm almost finished making, but is thrilled to still have the original too.
One note of caution. Make sure you stitch the fabric to the fusible side of the interfacing and carefully press to avoid letting the iron touch the interfacing or use a non-stick pressing cloth.
Hope this has been helpful. Have fun.