I am gluten free, but I'm also vegan, so I'm not low-carb.
I don't believe being vegan is necessarily healthful. In fact, I am proof you can be vegan and unhealthy. I became vegetarian when I was 2 or 3 years old; it was very young. It was for moral reasons then and still is now to some degree, but I honestly couldn't bring myself to eat meat if I wanted to. It's a mental thing. I am disgusted by it. I say that I am vegan because I've always been disgusted by eggs, which left milk, but I was having such a small amount of milk in my diet anyway and it started to gross me out more and more, that I cut it out, too. I'm not sure if this veganism is a phase that will return to vegetarianism or not. I've been grossed out by animal foods my whole lifelots of years of fighting with my parents over meat, eggs, and milk. I remember in 2nd grade, a kid brought cookies into school for his birthday, and I asked his mom if they had eggs, and I said I couldn't eat them. And the kid came up to me and said, "Don't worry you can't taste the eggs." Lol. I wouldn't even give into sweets I loved because of eggs, yet I had no allergy to them. I have severe OCD, and my parents think that's related to my disgust of animal products. I don't feel obsessed about it, though, just disgusted.
Anyhow, most of my calories come from carbs. I truly believe in the primal/paleo type diets. I just can't do it. I've read the science. I understand it. I believe it would be healthier for me (I'm overweight with high blood sugar and pre-diabetes).
I try to eat healthy, but when your calories are coming from plants, except for nuts, they're going to mostly be carbs.
As far as being gluten-free, it has helped me. Back in the days when the doctors in the US weren't familiar with celiac, I was tested because I had symptoms, and I was positive. I went gluten free for a year or so. I noticed some differences, but not a lot. I later got better testing that said I did not have celiac. However, I seem to feel better when I don't have gluten, much less acid reflux and seem to not have the pains I would occasionally get before. But I see no weight-loss effects from it. It's a subtle difference, but it does seem healthier. I think I also have a bit less bloating when I'm gluten free. Plus my sister is confirmed to have it, so it's likely I do to some degree.
Most of my weight problem is probably from 1) inactivity and 2) I take Seroquel at night which makes me into a ravenous monster. I'm slowly getting off of it. It was better than Zyprexa which made me gain 50 lbs in a couple of months. Seroquel also changes the way you metabolize things and raises your blood sugar.
Anyhow, good job on your GF/primal diet!