For solvent developers, like D-76, the stronger dilution will result in more softening of the grain and a bit less acutance; the weaker dilution gives greater acutance but more pronounced grain (Kodak states this very clearly...). Otherwise, dilution affects developer activity, which, as you point out, increases development time. The obvious advantage here is to keep development times from being too short, which can result in uneven development.
Another consideration is fog. Very active developers often produce more base fog. Diluting the developer can help reduce the amount of base fog.
Also, having less of the developing agent per unit of volume also can promote compensation effects where the developer exhausts in areas of high density before the developer in the less dense areas, resulting in a kind of proportional decrease in development as a function of exposure. This, of course, is dependent upon agitation technique; too frequent agitation and the developer in the denser areas has no or less time to exhaust. This is also somewhat developer dependent.
Best,
Doremus