Assuming you are not *bloated*and that really IS fat:
Abdominal (belly) fat is related with insulin resistance. Which is BAD!!! Insulin resistance is linked to Type 2 diabetes, heart disease, some types of cancers, etc. Insulin resistance, obesity, etc. is a growing problem worldwide, and although there may be other factors, it is closely tied with diet and/or lack of exercise.
While some possible reasons are hormone changes (i.e. menopause, hypothyroid, high adrenal levels) or insulin resistance due to previous starvation due to undiagnosed Celiac (ever notice how yo-yo dieters get fatter and fatter? That's one reason why!), it can also be the gluten-free diet itself.
Many people on the diet use the gluten-free replacement breads, cereals, baked goods, etc. These are LOADED with carbs, more so than gluten containing foods, and usually have little fibre. Fibre, found in whole grain breads, cereals, and oats, can prevent weight gain, Type 2 diabetes, and perhaps some types of cancer. Ever heard the term "Fibre is your friend"?
All of the above=weight gain, Type 2 diabetes, heart disease, the list goes on. I don't know if you use gluten-free products or not. Perhaps you don't. But if you do, you might want to stop. The gluten-free diet is NOT automatically a healthy one, unless you cut out processed foods altogether.
I personally use gluten-free products rarely. I eat mostly fish, beans, veggies, brown rice, nuts, and rarely, meat and fruit. I personally think that gluten-free replacement products (anything processed, really) are often not healthy. They're awesome for a treat, for sure though! I love gluten-free pizza, but I don't eat it everyday! The amount of carbs in that is INSANE. Get your fibre from brown rice and veggies, and stick to lean meats and fish. Make sure you are not drinking soft drinks (high fructose corn syrup) or eating junk food.
I would also ask your doctor to run a hormone panel, just to make sure everything checks out. However, this question seems to apear quite often, and I *personally* think it is linked with the gluten-free products that are marketed towards us. No one REALLY needs cookies, breads, pastas, flour, etc. Chocolate, well that's another story...hehe....

Hope you figure out why this is happening, and if you do need to change your diet, I am sending you support!

STARGAZER: I think you should also have your hormone levels checked. Do you feel like you have swelling or bloating? Do you have pain? Have you been tested for anything else? Like a C-diff infection? Or is it just plain old fat? There is also a good chance that you are severly insulin resistant due to the undiagnosed Celiac. In that case, make sure you are following a Type 2 diabetic diet, which it sounds like you are. You might also want to add Omega 3 supplements to your diet, and increase the amount of fish you eat. Look for wild salmon, it has less PCB's etc. Basically, you want to avoid all carb sources as much as possible. Salads, lean meat, fish, low startch veggies, gluten-free oats (if you feel safe eating them), and small amounts of brown rice are good. Make sure you get enough calories though overall. If you are still eating very few calories, that will all be stored as...you guessesd it! Fat!
Celiac...the gift that keeps on giving!