One reason could be that there is a natural fluctuation in weight during the menstrual cycle. Women typically gain 2 to 4 pounds prior to their menstrual period, and then lose these pounds after the period. Women on the stable hormone levels of birth control pills may not see this fluctuation and believe they have simply gained a few pounds. It should be reassuring that this weight is primarily increased fluid volume, not fat.
Another biologically plausible explanation is related to the progestin in birth control pills. Women naturally make progesterone right before their menses. Another time in a woman's life where progesterone is the dominant female hormone is the first three months of pregnancy. Many women report increased appetite during these times. It is possible, but we don't have enough research to say for sure, that the continuous dose of progestin in birth control pills affects some, but not most, women by causing an increase in appetite. Of course, what she does with that appetite is up to her. If she increases her intake of vegetables and fruit, she's not likely to see weight gain. If she increases her intake of high calorie snack foods, her results may not be as good!