In the first Friday the 13th movie, we saw that Jason's mother was the real villain. So what led the production house to switch to Jason rather than choosing his mother (or maybe choosing both of them) as a villain?
Jason Voorhees and his mother Pamela Voorhees are both portrayed as villains in the first movie. Mrs. Vorhees as the actual villain, revealed at the end of the movie to be the person who commits the actual murders. Jason appears at the end in a dream like sequence seen through the eyes of Alice, the lone survivor.
Jason was brought back in the sequel at the suggestion of one of the movies producers for the original film.
The filmmakers never intended to make this the launching pad for the series that followed. According to Victor Miller, Jason was only meant as a plot device and not intended to continue on his mother's grisly work.
The sequel actually shows Jason as a teenager/young adult for the first part of the film. Of course, Jason is seen five years later as a grown adult when he shows up to camp Crystal Lake to go on a murder spree to "guard" Camp Crystal Lake... and to avenge his mother's death.
Jason was actually never supposed to be in the films. He was only in the last scene in the original as a joke.
Initial ideas for a sequel involved the Friday the 13th title being used for a series of discontinuous films, released once a year, and each would be a separate "scary movie" of its own right. Phil Scuderi—a co‑owner of Esquire Theaters with Steve Minasian and Bob Barsamian and a producer of the original film—insisted that the sequel must have Jason Voorhees, Pamela's son, even though his appearance at the end of the original film was only meant to be a joke. Steve Miner, associate producer of the first film, believed in the idea, and he ultimately directed the first two sequels after Cunningham opted not to return to the director's chair.
Wikipedia explains it:
Many ideas were suggested for the sequel to Friday the 13th, including making the title part of a serialized franchise, where each succeeding film would be its own story and not related to any previous film under the Friday the 13th moniker. It was Phil Scuderi, one of the producers for the original film, which suggested bringing Jason back for the sequel. The director Steve Miner felt it was the obvious direction to take the series, as he felt the audience wanted to know more about the child who attacked Alice in the lake. Miner decided to pretend as if Alice did not see the "real Jason" in her dream, and Jason had survived his drowning as a boy and had grown up.