Progesterone cannot cause weight gain.

Estrogen causes cells to proliferate, including adipose cells, see here. These are also a source of estrogen, so excessive estrogen leads to excess fat, which in turn leads to excess estrogen, and so the cycle goes, see here, here, here and here. Estrogen also causes constipation by taking water from the gut and drawing into the tissues, thus causing edema for which it’s renowned, see here. Often the issue has to do with the dose being too low.