This is a good question. In many ways the whole nature/nurture debate is a false binary. In the end, it is always a combination of both nature and nurture. However, If we had to pick one, I would say that nature is the more important, as long as the nurture situation is not extreme, such as starvation, malnutrition, or other adverse circumstances. There are a few reasons for this.
First, if we look at things from a ethnic point of view, there is strong correlation between the size of a person and the ethnic stock of a person. This suggest that size is mostly determined by genetics. So, in some parts of Africa, people are extremely tall, and in some parts of South America, people are short.
Second, within these ethnic groups, some have access to suitable foods and other things that are necessary for life and still there are limitations. This shows that genetics have a powerful role.