Yes, makes sense to me. Your backache should get easier as you lose weight.
Some of the most common obesity-related problems include musculoskeletal and joint related pain.1 For people who are overweight, attention to overall weight loss is important as every pound adds strain to the muscles and ligaments in the back.
In order to compensate for extra weight, the spine can become tilted and stressed unevenly. As a result, over time, the back may lose its proper support and an unnatural curvature of the spine may develop.
In particular, pain and problems in the low back may be aggravated by obesity. This occurs for people with extra weight in their stomachs because the excess weight pulls the pelvis forward and strains the lower back, creating lower back pain. According to the American Obesity Association, women who are obese or who have a large waist size are particularly at risk for lower back pain.
http://www.spine-health.com/wellness/nutrition-diet-weight-loss/weight-loss-back-pain-relief
If you feel that this is not the case then ask to see an Orthopaedic Consultant.