Unbalanced May's contrived measuring system (10)
I believe the answer is:
asymmetric
'unbalanced' is the definition.
(I've seen this before)
'may's contrived measuring system' is the wordplay.
'contrived' is an anagram indicator.
'measuring system' becomes 'metric' (I've seen this before).
'mays' with letters rearranged gives 'asym'.
'asym'+'metric'='ASYMMETRIC'
(Other definitions for asymmetric that I've seen before include "kind of bars frequented by gymnasts" , "crooked" , "Not regularly shaped" , "Lopsided" , "Unbalanced" .)