I have no personal experience with the influence of a Water Fast on menses as I have just approached the menopause and my last menses have been sporadic.
I know from the literature that Water Fast may clear up some gynecological issues and it does not matter during which part of a monthly cycle the fast takes place.
A Water Fast usually reduces the pain during menses; However; it does not necessary reduce the amount of blood and the number of days of bleeding. Sometimes bleeding may be both much longer and bigger than usually due to the human body healing abilities facilitated by fast.
I hope you will reach both your weight goal and the overall healing; I believe that it is important to have a dream which assists in fasting.