Small animals face the biggest challenges in terms of competition for resources and predation by larger predators. Animals need resources such as food, water, light, habitat, etc. and they are in constant competition with other larger and smaller animals for such resources. For example, smaller herbivores live on plants, grass, etc. The same food is also eaten by larger herbivores and hence there is competition. Smaller animals are also under constant threat of predation by larger animals. For example, a rat is under threat from foxes and other similar predators. One can also think of food being out of reach of smaller animals if it is on taller plants.
Another challenge for smaller animals is traffic by cars. A large number of smaller animals are killed by cars, trucks and other vehicles every year. In comparison, larger animals face a lesser traffic threat.
Hope this helps.