I was having the same problem and but I just found the solution so I hope this clears anything up if there are still people playing this game:

take out your weapon with RT or R2. Go into first person mode with RB or R1 and then tap the Left Stick or L3 to draw your weapon without firing. While still in first person mode and with your weapon drawn you will want to hold down L1 or LB to aim down the sight of your gun. I know this is a hella old thread but I felt like clearing this up because I just found this out