This is a concern that we have heard from many women who are taking or considering taking birth control.
Birth control contains and effects certain hormones. One of the main examples of a hormone that is affected by birth control medication is estrogen, which can cause increased appetite and can also cause your body to retain more water. For that reason, certain birth control medication can cause weight gain, but only if it causes you to eat more throughout the day or cause you to retain more fluid (which isn't actually "true" weight gain – it's fluid weight). More recent birth control pills have lower levels of these hormones and likely will not be the reason for weight gain.
As always, please consult with your physician before trying any new dietary supplement while taking birth control medication.