No, Gearbox in their "infinite" wisdom changed it so that in BL2, certain loot doesnt drop till after you reach certain levels so that "the starting player isnt overwhelmed with loot". So in a way yes its biased but based on level not character.
"If your going to ask someone to save the world, make sure they like it the way it is" https://soundcloud.com/shake-like-e
I remember reading somewhere on the gearbox software website that the game is designed to introduce the weapon classes based on levels. So for example: assault rifles start to drop at level 2, shotguns at level 7 (made up numbers), etc. Sniper rifles were one of the later classes unlocked with launchers being the last. Just keep playing and you'll see some sniper rifles very soon.