Have preference towards parts of the Lesser Antilles (4)

I believe the answer is:

lean

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'have preference towards' is the definition.
I can't tell whether this defines the answer.

'parts of the lesser antilles' is the wordplay.
'parts of' suggests taking the first letters (I've seen 'part' mean this).
'antilles' becomes 'ean' (I can't explain this - if you can you should believe this answer much more).
The first letter of 'lesser' is 'l'.
'l'+'ean'='LEAN'

Can you help me to learn more?

(Other definitions for lean that I've seen before include "Without excess flesh" , "Containing little fat" , "Spare - list" , "David ..., director of Ryan's Daughter" , "Inclination" .)

I've seen this clue in the Evening Standard.

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