In Stranger Things 2, Billy is a new character, along with his sister Max. She has a purpose: she helps the party, but what about Billy?
His main actions were to pick up Max in his car and prevent her from seeing Lucas, bully Steve, and eventually fight him in the last episode.
We see some parts of his life from his point of view, but what is the use since he isn't central to the plot at all?
Matt and Ross Duffer (the creators/writers/often directors of the show) talk about this in the Netflix aftershow Beyond Stranger Things, Episode 1.
Billy was actually written in to serve as a specific type of character, the "human antagonist". Originally, they had intended this for Steve Harrington in season 1; but as the show evolved with the cast, they decided to redeem Steve near the end of that season.
They wrote the character Billy to play this role in a more irredeemable way. He was written to be the "human villain".
I'm purely speculating about this last part; but I assume his role as a villain will become more pronounced as the series goes on. From what I understand; they originally planned on using more episodes to end the season, so some character development had to be cut short.
I can offer a speculative answer.
Season two added other yet to be seen 80's allusions/references to it's ever growing pedigree of easter eggs.
One of the more obvious are things pertianing to The Lost Boys, a campy 80's vampire flick with elements of 80's hairbands and some Gothic Punk Rock. In that sense Billy may be like the Vampire antagonists...
Note: There is also a character named Max in The Lost Boys.
The Lost Boys is a 1987 American horror comedy film directed by Joel Schumacher and starring Jason Patric, Corey Haim, Kiefer Sutherland, Jami Gertz, Corey Feldman, Dianne Wiest, Edward Herrmann, Alex Winter, Jamison Newlander, and Barnard Hughes.
The film is also about two brothers who move to California and end up
fighting a gang of young vampires. The title is a reference to the Lost Boys in J. M. Barrie's stories about Peter Pan and Neverland, who, like the vampires, nevergrow up. https://en.wikipedia.org/wiki/The_Lost_Boys
The introduction of "8" and her motley crew of X-Men are one element that may relate to that.
Bob dressing up as a Vampire is another.
And Billy, might be another.
In addition Billy also reminded me of another Billy, Billy Hicks, from the 80's, played by Rob Lowe in St. Elmo's Fire. St. Elmos Fire and The Lost Boys feature plots where younger male characters are attracted to/seduce older female characters. This is similar to the plot with Billy and Nacy's Mom.
And lastly, season two made a point to open the scope telling viewers that this ongoing story isn't limited to Hawkings, as Nancy & Jonathan go out of town to talk to the conspiracy theorist, 11 leaves in search for 8, new commers from out of town, Max and Billy arrive in Hawkings, and the musical choices now include older than 80's tunes. The idea that Max and Billy come from somewhere else, *could imply that their backstory may eventually relate to the current story. In addition despite being an antagonist, the series makes an effort to show us one potential reason why Billy is the way he is (ie: his father) and *may imply character development and change of role down the line, much like Steve.
