Miss being sick? Not very (4)

I believe the answer is:
omit
'miss' is the definition.
(synonyms)
'sick? not very' is the wordplay.
I cannot really see how this works, but
'not' could be 'o' (I've seen this in other clues) and 'o' is located in the answer.
The remaining letters 'mit' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'being' is the link.
Can you help me to learn more?
(Other definitions for omit that I've seen before include "Exclude; forget to include" , "Leave something out" , "Fail to mention" , "Leave out, perhaps in error" , "Disregard" .)
