Burden being married troubles character (9)
I believe the answer is:
millstone
'burden' is the definition.
(millstone is a kind of burden)
'married troubles character' is the wordplay.
'married troubles' becomes 'mills' (I can't justify this - if you can you should give a lot more credence to this answer).
'character' becomes 'tone' (I've seen this before).
'mills'+'tone'='MILLSTONE'
'being' acts as a link.
Can you help me to learn more?
(Other definitions for millstone that I've seen before include "Grinding disc; wearisome burden" , "Heavy and inescapable responsibility" , "Heavy burden" , "something hard to bear" .)