The New Adventures of Batman bowed on CBS in February 1977 as a mid-season replacement. One major difference from the previous Bat-toons produced by Filmation, aside from live-action stars Adam West & Burt Ward brought in as the voices of Batman & Robin, was the debut of Bat-Mite, a imp from another dimension who was to the Caped Crusaders what Mr. Mxyzptlk was to Superman, a pest, except that Bat-Mite was the diametric opposite of Mxyzptlk. Whereas Mxyzptlk was pulling malicious pranks to get Superman's attention, Bat-Mite idolized Batman and wanted to join his team. He just couldn't take no for an answer.
To keep him around on a regular basis, head writers Chuck Menville & Len Janson gave him a schoolboy crush on Batgirl (Melendy Britt, replacing Jane Webb). However, the series opener, "The Pest", while marking Len Weinrib's debut as the voice of the Joker and Commissioner Gordon, also shines the spotlight on Bat-Mite, who wasn't appearing in the comics all that often by this point.
In effect, Bat-Mite was used to represent the curious younger viewers who shared his desire to be more helpful, though I'd imagine if the writers had been paying attention to comics of the day, they'd realize that Robin himself had developed an interest in Batgirl, which became an on-again, off-again plot device in the books for several years. I can just figure there were millions of teenage boys who felt the same way......!