What is hidden in DFT below frequency resolution?
Computing your DFT with a 0.5 Hz spacing is equivalent to appending your signal with 1000 zeros and then computing a 2000 point DFT. It should be clear that this adds no real information to the signal. Yet it can sometimes be useful.
What really happens by this zero padding is that you're seeing an interpolated version of your spectrum. This means that between each two &quot;valid&quot; points (at 1 Hz spacing) you're seeing one more that produces an interpolate, a potentially smoother version of your spectrum. The interpolation kernel is essentially a sinc function (periodified sinc to be accurate).
Depending on what you want to do with the spectrum, such interpolated results can be visually more pleasing and sometimes more clearly show things we would otherwise have missed.
In particular, if you have one harmonic signal and its frequency is not on the DFT grid, your DFT will not show one line but many. This is also known as the picket fence effect. This picture may be confusing and in cases like this, an interpolated version would show us more clearly what is going on and thus be easier to interpret. Also, this allows us to find the actual frequency with a better precision (NB: resolution is not improved by this, but precision is).
Here are two examples. In each example I considered N = 30 for clarity. For the first example we have a frequency of 5 Hz, falling exactly on the DFT grid. The 30-point DFT (depicted in red) gives just one line). An interpolated version is added with the dashed line just for clarity. You can clearly see the sinc-like interpolation kernels and how in the on-grid case we're sampling exactly the zero crossings, which is the reason we're seeing only one line.

In the second example, the frequency was chosen to be off the grid (between 5 and 6 Hz). Now the 30-point DFT shows many lines and it may be hard to see that these stem from just one harmonic if we only have those. Adding the interpolated DFT once more shows a very similar picture to before: We can see that it looks like one harmonic and we can much better spot its maximum.