I'm going to go a little further in answering this question, so I'd like to start with a bit more of Professor Trelawney's quote:
"I was saying that Saturn was surely in a position of power in the heavens at the moment of your birth... your dark hair... your mean stature... tragic losses so young in life... I think I am right in saying, my dear, that you were born in midwinter?"
In a book entitled The Manual of Astrology, first published in 1898, we find an interesting line:
[Mercury] in [Scorpius]:
Gives a short, mean stature, full and well-set but ill-made body, broad shoulders, swarthy, dark complexion, brown curling hair. Not in any way elegant or pleasing, yet ingenious and studious; very careful of their own interests, fond of the other sex, and partial to company and merry-making.
Interestingly, Scorpius is a winter sign (or at least, late autumn), covering the 24th of October to the 22nd of November. I don't have time to give this a full and proper investigation right now, and I'm not sure how Saturn fits in, but given the phrasing I have to suspect that this book was used as a source for Trelawney's line.
In this case, then, mean stature appears to be using mean in its adjectival sense:
3 (especially of a place) poor in quality and appearance; shabby
(of a person's mental capacity or understanding) inferior; poor
of low birth or social class