Is it normal for women in their early 20's to gain weight?

in high school i went from 110 lbs to 120 lbs and was distressed about that. I'm in my early 20's now and have gained even more weight (20 lbs!) even though i have maintained the same diet and exercise regimen. I've even stepped up my workout and am still not losing weight. I'm wondering if this weight gain is normal for most women around that age.