It's both. From memory I think it's about 3/4 nutrition and 1/4 genetics, but it's definitely partly evolutionary. Although scientists haven't nailed down WHY: it could be as simple as sex selection, or it could be that tall genes occur alongside some other beneficial mutation.
Under the right pressure adaptions can show noticeably within a few hundred years (ignoring really sudden stuff like the Black Plague) so there would definitely be some over ten thousand. But without being able to compare the two they may be harder to spot.