When I started doing calculations with the forums Buoyancy Calculator, things at first didn't seem to make sense to me, either. Then I tried this practical demonstration. After a weekend of diving, I had empty tanks -- I had breathed the tanks down, I selected a 12l and a AL80 that both had 500psi left. I rigged them both up and took an extra (full) tank with out to the dive training platform at 15 ft depth. I tied the two empty tanks to the platform, so they didn't float away. I was already wearing correct weight for diving with an AL80. The empty AL80 was upside down, and ever so slightly positive buoyant (the valve weight and rigging straps just about balanced the positive buoyancy of the tank. I dumped all the air from my wing, and stood my full tank on the platform. I, too, was neutrally buoyant. I could clip that empty AL80 on with no change in buoyancy.
Next I checked out that 12l steel. It was laying sideways on the platform. The slight current could move the base of the tank in an arc around the point where the shoulder rested on the platform. I swapped empty tanks, and now I was slightly negative. I could compensate by breathing off the top of my lungs, but dropping 3 lbs fixed things up.
I proved to myself that I really did only need to change carried weight by that 3 lbs, even though the big tanks weighed 6 lbs more empty, and contained 2 lbs more air full.