stabilising the zip in a delicate fabric

When stitching an invisible zip into a delicate fabric, it's a good idea to stabilise the fabric at the stitching line somehow, give it some oomph to help guard against ripping. Generally, patterns recommend using commercially purchased bias binding or tape, which is sewn to the seam allowance to double the thickness of fabric at that point. Me being kinda ~~stinge-y~~ I mean thrifty, ahem! I usually snip a strip of the selvedge off to use.
Why? several reasons...
The selvedge of any fabric, even delicates, is usually surprisingly strong and quite stable compared to the body of the same fabric.
Particularly with sheer fabrics; the selvedge, being exactly the same colour of course, will blend in perfectly and won't show through to the right side of a sheer fabric at all. This is a big plus if your fabric is an unusual colour.
Also, you are making good use of the scraps that you would probably toss out anyway, which is more economical than not, yes??
Just stitch it down to the wrong side of the garment, as close to or just within the seam allowance. If your fabric is super delicate you could fold it over, or use a couple of strips layered together, giving you triple thickness fabric at this point...

Sew in the zip as normal...

Don't worry about those fluffy messy looking edges, because once the lining has been stitched to the zip tape you can't even see those scrappy edge bits anyway.