I have seen these restrictions, usually between 5'x and 6'x. I think BA did it when I applied for their sponsorship course back in 2001. Below is from the current Direct Entry BA requirements:
"Height between 1.57m (5'2") and 1.91m (6'3") with weight in proportion to height (height is accurately determined during the assessment process). Qualified pilots who are taller than 1.91m may submit an application but will be required to undergo a functionality check to confirm their ability to meet the requirements of the seating"
Not sure about others.