I recall reading that Alexandra was concerned about weight issues re: her two youngest daughters. Whereas Olga and Tatiana were naturally slim, Marie and Anastasia tended toward "baby fat." Marie eventually shed most of her pudginess, but during their captivity Anastasia had hit a point in which she was adding weight but not growing any taller. (The lack of real exercise couldn't have helped, either.) Remember one of the plays the family performed while in captivity, in which Anastasia elicted laughs from everyone--her mother included--when her rather round bottom was suddenly displayed, solidly encased in her father's underwear?
Whatever weight issues Alexandra had as she grew older were related to her childbearing and relative inactivity. But Nicholas did work hard to keep his weight down--he loved to exercise anyway, but undoubtedly was also motivated not take on excess weight as had his father and several uncles . . . especially since he didn't have their height and larger bone structure.
When Marie is often referred to as resembling her father's side of the family, I think much of this is in reference to her stronger, more solid build, especially in contrast to the slender builds of her elder sisters.