I come down with a severe infection after losing a few pounds on a sensible diet.?

I've had viral and bacterial pneumonia, strep and staph infections. Every time I get sick - I gain weight. Every time I decide I'm well enough to lose weight - I get sick. I can stay healthy by over eating. Help! I'm 100 pounds overweight and I'm afraid to lose any weight for fear of becoming ill again. I'm female and 60 years old.