True anatomical/physiological explanation for "metaphysis" etymology
meta-:


  word-forming element of Greek origin meaning 1. "after, behind; among,
  between," 2. "changed, altered," 3. "higher, beyond;" from Greek meta (prep.) "in the midst of; in common with; by means of;
  between; in pursuit or quest of; after, next after, behind," in
  compounds most often meaning "change" of place, condition, etc. This
  is from PIE *me- "in the middle" (source also of German mit, Gothic
  miþ, Old English mið "with, together with, among"). Notion of
  "changing places with" probably led to senses "change of place, order,
  or nature," which was a principal meaning of the Greek word when used
  as a prefix (but also denoting "community, participation; in common
  with; pursuing"). (Etymonline)


physis:


  The growth plate, or physis, is the translucent, cartilaginous disc
  separating the epiphysis from the metaphysis and is responsible for
  longitudinal growth of long bones. (The Royal's Children Hospital Melbourne)


Anatomically and physiologically, meta- in metaphysis means next after physis (growth plate or epiphyseal plate) and refers to the changing (growing) part, which is in between the non-growing parts of a long bone (diaphysis and epiphysis): 


  The metaphysis is the wider portion of a long bone adjacent to the
  epiphyseal plate. It is this part of the bone that grows during
  childhood; as it grows, it ossifies near the diaphysis and the
  epiphyses. (Orthopaedicsone)




Picture: Parts of the bone (Radiopedia, Creative Commons license)