In the original Big Hero 6 comics from Marvel, Hiro had a crush on Honey Lemon, but the two were never really involved in a romantic relationship. Early versions of the film adaptation considered portraying Hiro's crush on Honey, but it was ultimately scrapped.
In the movie, Honey is always caring towards Hiro, making sure to always be by his side when he needs her. As it is with her personality, Honey Lemon shows a lot of affection towards Hiro, including giving him hugs, talking to him earnestly and sweetly, and even giving him kisses on the cheek when they first met. As with all other pairings within Big Hero 6, there is never any canon confirmation (at least in the final version) of romance between Hiro and Honey, so fans are left to interpret it however they wish---some see them as friends, some see a brother/sister-like relationship, and some see romance.
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