The granularity of a film is essentially fixed during its manufacture. This is why Kodak can specify a RMS granularity of each of its film. The granularity can be reduced somewhat by the choice of developer. Obviously a solvent type developer will produce finer grain.

Now the perception of grain is influenced by several factors among them the Gamma or Contrast Index of a negative. The lower this value the less grain perceived by the human eye. When film is stand developed it is usually developed to a lower Gamma than normal and so will appear less grainy.

There is only one reason to use stand development and it is usually described in manuals on the Zone System. That is to reduce the overall contrast of a contrasty subject to match the tonal scale of a particular paper. I can't think of a single subject in photography that is the source of so much speculation, unfounded claims and general folderol than stand development.