You will need a third-party program for that, as you cannot adjust the curves in the game.
These two appear to be the most popular "independent" programs:
Joystick Gremlin and
Joystick Curves. Then there are programs that come with the stick, like Thrustmaster's T.A.R.G.E.T.
By adjusting the curves, you are changing the effect of the input from the joystick to the program. Without curves, the input is linear, which means 10% movement on the stick will give 10% input to the program, 50% movement will give 50% input, etc.
What you probably want is to make the initial movement do less input, and then ramp it up towards the outer limits of the joystick axis. That will give you more fine control with small joystick movements, while still have full range when pushing it all the way.
I use Joystick Gremlin, and this is what I have set up for the curves on my Pitch and Roll axis:
Without curves applied it would look like a straight diagonal line.
Note that curves can be very individual, for all axis. So I recommend you play around with it, set curves for three axis, then play with that for a few weeks. If something feels off, adjust the curve, and play with that for a few weeks. Eventually you will figure out what curves are best suited for you and your joystick.
I still haven't nailed down mine the way I want them [where is it]