Currently - the only weight gain is implemented for characters in the Weight Craft training segments - oh and a few random encounters. Once implemented - all romantic interests will have a weight gain path. I'm fleshing them out one by one and concentrating on their "core" content before I implement the weight gain mechanics. There is a tonne of weight gain related content technically already in the game - its just currently locked at the moment by not having implemented the features to unlock that content.
But if you want names specifically - of the characters introduced so far: Brynhild, Rhianon, Thalia, Artemis and Elaris (those last two you can encounter in the Academy but they've not had proper introductions yet)