There's no way to make a featherweight sew extra-stretchy materials. It just won't do it.

You need a machine that can do a "stretch stitch" and a "zig-zag", also "blind hemming". Almost any newer machine would work for this: Pfaff, Bernina, Brother, Singer, really almost any brand. Check used machines on Craigslist or FaceBook, and ask local dealers if they have any. Take a sample of the stuff you want to sew with you to test the machines.

Keep the Featherweight for the stuff it does well, or sell it to a quilter.

A machine that can zig-zag can sew stretchy material You can use a zig-zag stitch, or whatever the machine manual suggests for sewing knits. If yo want to finish the edges (I'm guessing that's what you mean by edging) your best bet is a serger. You can use a zig-zag, we did that for years before sergers were cheap enough so that most seamstresses and seamsters bought them.

You might try a walking foot & very, very short stitch length. I used to sew stretch fabrics on my mom's old featherweight using 20 stitches/inch or more, which builds stretch into a straight seam, tho not as much as zigzag.

A walking foot is pretty useful for a number of things & costs less than a whole 'nother machine, so it may be worth trying...

http://www.craftsy.com/blog/2014/07/how-to-use-a-walking-foot-for-garment-sewing/