In animals, at least, the reason for maturation has to do almost equally with genetic limitations and environment. It's been observed that animals of the same species and even the same generation with some of the animals experiencing severe climatic conditions with greatly reduced food availability can be noticably smaller than those with normal, unrestricted food. If the conditions continue for extended periods of time, genetic limitations can develop that affect the entire species as to size.
This interesting question also has something to do with the surface area to volume ratio of the body. Each species has an average body size that works well in its environment, and the body's organs, such as the lungs and heart, are designed to work best at that size and weight. Growing larger could lead to a loss of efficiency. This is especially important for warm-blooded animals, whose food needs are high. Also, when the animals become mature, the extra energy that was used in growing can be redirected toward reproduction and the care of their young. Size appears to be inherited: micro-evolution would select animals that grew to an optimally efficient size and then stopped the growing process... In my opinion....