I view its etymology like this,

              Lil B
    (based ≈ doing your own thing (in a good way)
             not swayed by critics)
             ↙           ↘
       Gen Z             4chan
   (based ≈ cool)        ("based and redpilled"
                          ≈"unswayed by pop rhetoric"
                           and "sees the world beyond the 'illusion'", resp.)