There are a couple of issues that should be addressed concerning her weight gain.
1) Too much fat or calories consumed or in her diet. She is nearing the senior age now and being placed on a light or restricted diet may help. Most times dogs as they age become less active, do not need as many calories to sustain life, yet cannot adjust the amount they eat own their own. If she receives any treats or table snacks this must be added to her daily caloric need and usually throws them over the recommended amount. Exercise is another very important factor. Daily walks will help or at least twice daily play (fetch) in the yard.
2) Hypothyroidism: She is right at the age where this can develop. A dog just does not burn up the calories as their metabolism has significantly slowed. Even if the dog eats the same amount or less they still seem to either gain weight or are not able to lose it. Other common symptoms are lethargy, joint pain, weakness, constipation, skin issues (dry, flaky), neurological symptoms like seizures, and even hair loss.
3) Cushing's Disease: This is where there is an overproduction cortisol, a steroid. This can cause weight gain or a pendulum/bloated like appearance to the stomach. Most dogs will also pant excessively, drink excessively, urinate excessively and many times just pace. Their demeanor may change and they may be a bit anxious all the time.
I would try to adjust the diet first. Measure the amount of food given to each dog so that you know who is getting what. Also consider changing the diet to a light formula of the same brand. Read the recommended amounts on the back of the bag for your dogs weight and decrease this by 20% since they always go for the higher amounts. Treats can consist of kibble, carrots, green beans and peas only. See if this helps. If we end up still struggling with our weight I would have her checked by your veterinarian and get a blood profile performed to include thyroid.
As for the scooting, the most likely culprit are the anal glands. The anal glands are located on either side of the anus. When they are functioning properly they express a few drops after each bowel movement. In the wild these drops are actually used as a specific scent or marker for other dogs to know who was there. As a normal housepet these glands can just become an annoyance especially when they become clogged or infected. They can do this as a result of too small of an opening, allergies and inflammation or because the stool is not bulky enough to force the glands to express. Once they become full they are very uncomfortable for the dog. There is also high potential for infection as we all know this isn't the cleanest part of the body. If they are infected they can rupture through the skin. The dog scoots in hopes of relieving the this impaction, most times to no avail. Aren't you glad we don't have these glands, can you just picture that?
It would be a good idea for you to take your dog to a veterinarian to express the glands for you. They will also determine if an infection is present and prescribe antibiotics to help clear it. You may request they teach you how to express the glands if the condition persists.
In the future it would be helpful to include canned pumpkin to her food as this increases her fiber content and bulks up the stool. You may also want to consider a higher fiber diet in the future aswell.