Meagre as everything short and fat (6)

I believe the answer is:

grease

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'fat' is the definition.
(animal fat for cooking)

'meagre as everything short' is the wordplay.
'meagre' becomes 'gre' (I can't justify this - if you can you should believe this answer much more).
'short' indicates taking the first letters.
The first letter of 'everything' is 'e'.
'gre'+'as'+'e'='GREASE'

'and' is the link.

Can you help me to learn more?

(Other definitions for grease that I've seen before include "A thick oily substance" , "Musical - lubricant" , "Travolta's 1978 film" , "Lubricate (-ant)" , "bribe" .)

I've seen this clue in the Sydney Morning Herald.

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