When Heather was (against her will) working for Alvin, Astrid was the very first person to suspect that the story Heather told everyone about how her island being invaded by pirates. Her suspicions were proven right when she saw Heather talking with Savage, Alvin's second-in command, on the Dragon Academy's secrets. The other members believed Astrid was just jealous of the attention Hiccup was giving the black-haired liar, until they realized that Heather ran off with the Book of Dragons and Astrid's Nadder Stormfly. They capture her (losing the Book of Dragons in the process) and lock her up, Heather coming clean that her parents are being held hostage. Astrid disguises herself as Heather, the other tamers set up on Outcast Island to pick her up as soon as she takes the book. Astrid realizes that Heather was telling the truth and manages to escape using a rogue Monstrous Nightmare. Alvin tries to stop them, only to be saved by Heather riding on Stormfly. They all escape Outcast Island, they wish Heather well and gain a new friend in the process.
In Race for the Edge, Astrid and heather seem to make a connection with each other more so than with any of the other riders, and seem to have more in common than originally anticipated. Astrid helped Heather escape the others when she was clearly uncomfortable with them, and they socialized with each other like old friends. They discuss mutual interest in dragons, battle, weapons and even boys, Heather teasing her over Astrid's denial of liking Hiccup. When Heather joined the Dragon Hunters, Astrid was the only one who knew of her true loyalties, acting as each other's mutual informants and the only ones they could trust. Since joining the riders, Heather shares similar roles to Astrid as their combat-expert, sharp-class trainer and object of Snotlout's misguided affections.
Being the only other girl their age (aside from Ruffnut) to be featured in-canon on Berk, fans like to use the conflict between the two and eventual friendship as a gateway for emotional and sexual tension between the two, making them a couple. Other than that, Heastrid usually arises as part of a demand for a Yuri pairing same as Ruffstrid.
Though historians have shown that homosexuality between Viking men (or "fuðflogi") was frowned upon to a certain extent, is is unclear to what extent homosexuality between women (or "flannfluga") was viewed as, so writers have little historical reference to base the relationship upon, deciding what happens on their own.
Note: Please add only ones that are part of the RotBTD fandom