Can natural hormone replacement therapy cause weight gain?

Yes if unbalanced. The key to natural hormone replacement is balance. If balanced you should gain weight no more easily than you did when you were younger if you are eating a proper diet and exercising to maintain adequate muscle mass. Muscle mass controls your metabolic rate. Too much Estradiol or Progesterone can cause weight gain. Too much testosterone can boost appetite.
Yes. Unfortunately some patients do gain weight (often in their abdomen, breasts, and back of their upper arms) with estrogens, whether or not the preparation is "bio-identical" or a synthetic analog. Balancing Estrogens with Progesterone and/or androgens often reduces this effect, which is dose-dependent. Prior weight gain to birth control pills sometimes predicts the same weight increase with hrt.