Height increased dramatically last century. See one of the Top Ten Science Stories of 2013 from Natural History Museum website:
"9. Evolution pushes on as European men grow taller, September
Good food, better hygiene and health, as well as smaller families with fewer mouths to feed, have meant that the average height of men across 15 European countries has increased by nearly 11cm."
Before we understand the reason for this, it would help to narrow down the time that height is set, as any environmental factor operating outside this window can immediately be discounted. So when do these factors have their effect? Is it at pre-conception; pregnancy; birth; infancy, childhood; adolescence; adulthood? A similar consideration applies to social class differences in height, IQ, health, etc. When do these start, and do they widen with age?