Honours ultimately desirable, carrying a lot of weight (5)
I believe the answer is:
obese
'carrying a lot of weight' is the definition.
(I've seen this in another clue)
'honours ultimately desirable' is the wordplay.
'honours' becomes 'OBEs' (Order of the British Empire awards).
'ultimately' indicates one should take the final letters.
The final letter of 'desirable' is 'e'.
'obes'+'e'='OBESE'
(Other definitions for obese that I've seen before include "likely to tip the balance?" , "Too chubby" , "Excessively fat" , "Extremely portly" , "Enormously portly" .)