First, you should try living mulch, which is a growing plant. It stays in its place for a longer period of time and is naturally anchored to the soil. It also provides nutrients to its surrounding soil and also helps in stopping the growth of weeds. People usually use this type of mulch in their yards or lawns.
Make sure you have applied your mulch to a proper depth that should be almost 3 to 4 inches. You should also apply thick mulch as a thin layer cannot prevent the growth of weeds. If the weeds start growing, the mulch will not be able to stay in place for a longer period of time.
Furthermore, thin layer of mulch leaves many bare spots on the surface of the soil that invites weed growth. So, you should not leave any space empty and try to cover it by applying mulch.
You should also use heavy material which will help the mulch to stay in place despite being rolled by the foot of animals or by a strong wind. People normally prefer inorganic mulch like stone or gravel that tend to stay on their place and do not get scattered easily.
However, according to the research of Clemson Cooperative Extension, stone mulch is not suitable for all types of plants. For some, it is harmful and you need to consult with a relevant professional or specialist before applying stone mulch.
You should avoid using plastic mulch or anchor landscape cloth as these are very light materials and can easily be dislodged by strong wind and animals.
Make sure you get complete information about the application of mulch according to the season. Usually 5-inch depth is recommended in the fall and it varies according to the weather.