Not as much as I'd have expected.
CO2 has a molecular mass of about 44; He, 4; O2, 32. So the volume would increase by (44-4)/(44-32) = 40/12=3.33-fold. Cube root of that is about 1.5, i.e., the balloon has to be about 50% bigger in all directions.
Though actually, we'd probably be using hydrogen, not helium. (This is Mars. It won't burn.) Hydrogen molecules leak less than helium does. There is a very slight advantage due to a lower molecular mass of 2.
Still... compressed tanks of gases are heavy. If they leak, you can't generate more. Silly as it sounded at first, I now actually wonder if you might do well to generate O2 on Mars and use that to lift your balloon/dirigible. Yes, the balloon has to be 50% larger, but not having to deal with hydrogen or helium would be a Big Deal.
And, of course, technology to extract oxygen from the atmosphere of Mars might eventually be of biological utility.
As to volume needed : on Earth, a cubic meter lifts about a kilogram. On Mars, the atmospheric density is (I think) about 1% of that, so you'd be talking about needing a hundred cubic meters to support one kilogram, or about 333 m^2 if you're using O2. Which would have to include the mass of the balloon, too. I don't know enough about balloons to say if that's stupid to hope for.