My dog, Molly, and I eat pretty much the same thing: a lacto-paleo, nutrient rich diet that I hope will heal our minor cavities. I've lost one to two pounds, but Molly has gained weight: she's 73 pounds and I had to loosen her collar. Of course, it may be that her owner is simply feeding her too much; even on a low-carb diet, some people and dogs gain weight with too much food. It could also be a thyroid problem, which the vet is checking.
Looking around the web, it seems a 60-pound dog (which I'd like Molly to be) should eat around 1100 to 1200 calories per day. Molly may be eating a little more than that, but she probably needs fewer calories on the diet we follow. Another site recommended about 1.25 pounds of meat per day for a 60-pound dog. (The vet recommended diet dog food to get the calories just right. I didn't ask him if he weighed out his own food and counted calories to avoid going over.) In any event, I will give Molly somewhat less food than I have been and not assume she wants a snack if she bugs me. But if she really does seem to be hungry, I'll give her a small snack. And if she doesn't lose weight, I won't put her on a starvation diet.