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Obesity affects your back in many ways causing eventual back pain:

A- obesity stresses intervertebral discs:
1- obesity could increase the mechanical load on the spine, Obese people may also be more liable to incur accidental injuries.
2- obesity may cause systemic chronic inflammation by increased production of pain mediators.
3- Abdominal obesity ( more than generalized obesity ), hypertension, and dyslipidemia all produce atherosclerosis — that- could cause malnutrition of the disc cells and degeneration that sure causes low back pain.
4- Abdominal obesity causes a shift of the center of gravity forward and this stresses discs more. 
5- Spinal mobility decreases with increasing body weight, which may interfere with disc nutrition.

B- obesity stresses facets:
1- Obesity increases lumbar lordosis, which in turn stresses facet joints accelerates its degeneration, and causes back pain 
2- outer abdominal fat (OAF), OAF significantly increases with higher degrees of FJ arthritis