Joseph, how is it not obvious? If the body is not getting the nutrition it needs to grow properly, it won’t. That’s why in the middle ages people were unnaturally short, and now with proper nutrition they have shot up. And a child starved of calories and nutrients will not enter puberty for a long time.
The same applies to illness. A body that is fighting illness cannot devote the resources necessary to develop normally. I know a pair of technically identical twins who look nothing like each other, because one went through a serious illness and basically skipped at least a year of growth, while the other was healthy and grew normally.