Bang! 6 Player Problem - It's unbalanced one way or another.
From reading your question and responses in the comments I would say that 100% you are playing the game in the spirit that it was designed.

Rules


  4 players: 1 Sheriff, 1 Renegade, 2 Outlaws
  5 players: 1 Sheriff, 1 Renegade, 2 Outlaws, 1 Deputy
  6 players: 1 Sheriff, 1 Renegade, 3 Outlaws, 1 Deputy
  7 players: 1 Sheriff, 1 Renegade, 3 Outlaws, 2 Deputy


Killing a player


  Eliminating a character
  When you lose your last life point, you are eliminated and your game
  is over, unless you immediately play a Beer (see below). When you are
  eliminated from the game, show your role card and discard all the cards you
  have in hand and in play.
  Penalties and Rewards
  •    If the Sheriff eliminates a Deputy, the Sheriff must discard all the cards
  he has in hand and in play.
  •    Any player eliminating an Outlaw (even if the eliminating player is
  himself an Outlaw!) must draw a reward of 3 cards from the deck.


End Game


  The game ends when one of the following conditions is met:
  a) the Sheriff is killed. If the Renegade is the only one alive, then he wins.
  Otherwise, the Outlaws win;
  b) all the Outlaws and the Renegade are killed. The Sheriff and his
  Deputies win.


I will break down the conditions that need to happen in order for the renegade to win.

4 Player Game:


The renegade needs to kill (or assist) both outlaws
Once both outlaws are dead the renegade needs to kill the sheriff


5 Player Game:


The renegade needs to kill (or assist) both outlaws
The renegade needs to kill (or assist) the deputy
Once both of those are done the renegade needs to kill the sheriff


6 Player Game:


The renegade needs to kill (or assist) all three outlaws
The renegade needs to kill (or assist) the deputy
Once both of those are done the renegade needs to kill the sheriff


7 Player Game:


The renegade needs to kill (or assist) all three outlaws
The renegade needs to kill (or assist) both deputies
Once both of those are done the renegade needs to kill the sheriff


Note with expansions there is also an 8 player game that adds in a 2nd renegade

8 Player Game:


The renegade needs to kill (or assist) all three outlaws
The renegade needs to kill (or assist) the deputy
The renegade needs to kill (or assist) the other rendage
Once all of those are done the renegade needs to kill the sheriff



  I think it's a good rule of thumb to act as a deputy early, but working with the other deputies to buff the sherif is not always a good idea. It can oftern put you in a position where its you and the sherif and but the sherif's sitting pretty with barrel/mustang/hideout or something.


What you are forgetting or ignoring is that with no matter how many players (4-8) a game is setup with a renegade will have to ensure that every player but the sheriff is killed in order for them to have a shot at winning. So it will always come down to a situation where the sheriff and renegade are in a dual so there is no reason not to help the sheriff kill the outlaws. In fact if you do a convincing enough job you might get the sheriff to kill the deputy which would make them lose all their items and become easier to kill.

Another thing you should remember is that not all games are designed to be perfectly balanced for one side or the other and in truth the real role that has reason to complain is the renegade since they can only win when everyone else is dead.

I would also like to point out that in a 6 player (or larger) it is very possible for the players later in play order to be killed before they even get a turn so I would not say this game considers balance at all.