Conservative MP has issues carrying weight (8)
I believe the answer is:
emphasis
'weight' is the definition.
(thesaurus)
'conservative mp has issues carrying' is the wordplay.
'carrying' says the answer is hidden in the clue.
'EMPHASIS' is hidden in the letters of 'conservative mp has issues'.
(Other definitions for emphasis that I've seen before include "Stress or significance" , "Stress, accent" , "Weight" , "Special importance or prominence given to something" , "Stress laid on, eg, words" .)