How old is your girl?
How much does she weigh?
Is the hair or skin oily or flaky?
You say she wants to lick herself there, can she reach that particular area?
Being overweight this area is difficult for her to groom. This being said her skin will become flaky and there will be an oil buildup and will start to itch. Essentially, she cannot reach it. So when you are rubbing, scratching, or brushing it she will lick, she may even chew on her own paws while you are brushing. It is like that spot right in the middle of your back that you cannot reach but you get someone else to do it and wow isn't that a relief. The first thing to do is make sure there are no fleas on her. She may have an allergy to fleas and just one bite can cause a very itchy reaction. She could actually have airborne or food allergies. Doing a trial of an antihistamine may prove beneficial. Chlorpheniramine at a dose of 1/2 tablet twice daily for at least a week to decide one way or another if it is going to help would be recommended. I would also consider a diet change to something all natural. Nutro or Eagle pack or even a hypoallergenic diet from your vet. A food trial should last at least 8 weeks before deciding it isn't going to help. Avoid all treats or snacks during this time. The biggest thing you can do for her is to brush her everywhere including this area twice daily. Bathing or soaking the back end in an aloe and oatmeal shampoo is a good idea once weekly. Remember she cannot reach here to clean or groom herself you will need to help her to do this.
This is going to be a trial and error process in getting down to what is wrong. Make sure the veterinarian ran a thyroid profile on her as hair loss can be a symptom of thyroid problems and if she starts to lose weight then take her right back in for a recheck on the thyroid.
Her bottom may be a bit sore too. Cats who are overweight can develop issues with constipation and obstipation. This can become a serious issue because the nerve function is weak and they are not able to express bowel movements normally. Something else to keep an eye on in the future.
Please let me know if I can be of further assistance.
Something I neglected to include in the above information is that I would recommend starting her on omega three fatty acids. You can get this from your veterinarian or purchase this at any pet store. These fatty acids are good for the skin and coat and also have somewhat of an anti inflammatory affect which may help to improve her condition.