Ive heard that people born in the past 100 or so years are taller than people born before then because of better nutrition. So if the royals were presumably better fed than their subjects for generations, would they have been noticeably bigger?
This is one of those urban fallacies.
People weren't demonstrably taller or shorter in the past than now, it does appears that way because doors were smaller. In reality that was because it was easier to heat a room if you limited the size of doors and/or windows.
From history and legend, we hear of tall people. Edward I was called Longshanks, because he was so tall. Maelgwn Gwynedd was known as Maelgwn Hir (the tall) for the same reason. Then you get Little John from the Robin Hood legend - little being ironic for gigantic.
In archaeology, remains have been found from burial sites throughout history (and occasionally prehistory too). The people uncovered weren't noticeably taller or shorter than their counterparts today, regardless of class.