Since alcohol is fat soluble, one's weight has more to do with one's alcohol tolerance than one's height does.
Student or Learner
In the question, 'How much could he possibly drink, a man of his stature?', can stature be replaced with height so this still sounds natural?
Is stature more sophisticated or old-fashioned way to say height in this example?
When referring to how much one can drink, do you mention their weight as well? Are there any other traits that can be used for this sort of description?
I think the writer was just trying to think of a fancy way of saying 'size'. As MNY said, height is of limited relevance.