A mulch helps to keep the soil moist near the surface, where dogwood roots are most active. It helps to prevent the growth of weeds. And as the mulching material decays it releases nutrients for use by the dogwood tree. Use wood chips as a top-dressing , rather than shredded bark mulch. The wood chips stay loose and allow rain to penetrate.
Shredded mulch tends to cake at the surface so water runs off.
Mulching with composted or partly-composted leaves is extremely beneficial for all plants, especially native trees like dogwood and redbud. Using these natural products provides at least some of the complex woodland micro-organisms that would be found in rich woodlands. There are commercially-available supplements that attempt to replace some of the mychorrizal soil components. If you maintain an adequate mulch around dogwood trees, few weeds should grow there. Those that do grow can easily be pulled by hand.