Weight control is important to maintaining a healthy back. Additional weight, especially in the stomach, shifts your center of gravity forward and puts additional strain on your back muscles. It is recommended to keep within 10 lbs. of your ideal weight for a healthier back.
However, it is possible to be too thin. Extreme thinness can accompanied by low bone mass, putting you at risk for osteoporosis.
The best recommendation is to eat a well-balanced diet in moderate quantities. Extreme changes in diet and frequent fluctuations in weight can cause loss of muscle and bone density in addition to fat. Lost fat and muscle can come back, but bone could be gone forever and put you at greater risk for osteoporosis, which can affect your spine.