According to Webster's Dictionary "middle" is both a noun and an adjective.
adjective - means central, intermediate, average in size, quality or status, e.g. the middle rung of a ladder / middle-lfe
noun - means a place, moment or thing that occupies a middle position, e.g. the middle of the week / the middle of my life / he is standing in the middle of the crowd.
Height - we use: low/short, mid-height/middle height/average/medium height, tall/high
Age - we use: baby, infant, child, pre-teen, adolescent, teenager, young adult, adult, middle-aged/mid-aged, senior.