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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)