I use flours other than rice. I use Sorghum, Millet, bean, mixed with corn and tapioca starch -- they are hearty and just have more to them.
You diet sounds great, I went GF and it hasn't helped my weight at all (but I'm also not GS or CD, a few of my kids are).
I would 2nd the suggestion of thyroid. If you are Celiac, the genes involved are also linked to auto-immune thyroid disorders such as Hashimotos and Graves which would cause weight loss.