The bottom line is that you don't have to gain weight while on progesterone. You can use lifestyle changes to prevent weight gain including tracking your food intake and energy. For more info on this topic, along with other questions about weight gain with contraceptive hormones, see our article called Weight Gain and Birth Control Pills.
Always remember, the only direct cause of weight gain is consuming more calories than you burn – period. Weight gain cannot happen unless this takes place. That said, medications can affect your appetite and energy levels, leading you to consume more calories than you burn. But at the end of the day, you DO have control over your weight.