I'm assuming that you are doing machine embroidery? If you hoop your fabric, don't over tighten. The embroidered portion will remain stretched, and when you un hoop, the rest of the fabric will relax creating puckers. I'm a non hooper. I hoop my stabilizer, then lay the fabric on top, using a spray adhesive and or pins (far away from the embroidery). Use the smallest hoop that will accommodate your design. You can also experiment with different weights of stabilizers.
The best bit of advice I got when I took lessons with my new embroidery machine was to make intelligent choices on the design/fabric pairing. Heavy, dense designs will be most successful on heavy dense fabric which will support all those stitches. Choose less intense stitch designs for lighter fabrics.