Date: 7/12/12 11:56 PM
They'd do a burn test, which you can easily do yourself. I'm having a glitch with my iPad copy and paste, but google "identifying fibers and fabrics"! It's a PDF with how-to and a burn chart.
On second reading, you're looking for the weave, not the fiber? if you determine the fiber, ie polyester, then you know it's a smooth-back poly crepe double knit.
Email Mood Fabrics, Sawyer Brook, Gorgeous Fabrics and Marcy Tilton and ask if you can send a swatch for ID; they all carry a very good collection of bottom-weights so would be likely to know what it is.
Hope you find lots more, whatever it is!
-- Edited on 7/13/12 0:01 AM --
I heart Panzy, Pfaff Creative Performance, the sewing machine love of my life!
And Baby (Enlighten serger), Victor (BLCS), Rupert (Pfaff 2023-knits expert) Ash (B350SE-Artwork), Kee (B750QEE-Panzy's BFF), Georgie (B560-Kee's baby sister) and the Feather-Flock!
Most of all, I heart Woo (HimmyCat). Until we meet again, my beautiful little boy. I love you.