The most common and most likely answer to this crossword clue is the 9 letter word ENDOMORPH
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Buddy explains!

The straight part
We know that "a fat person" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a fat person = endomorph.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ENDOMORPH mean?
ENDOMORPH noun- A mineral, especially a crystal, enclosed within another
- A person of the endomorphic physical type, characterised by big bones, round face, large trunk and thighs and a naturally high degree of body fat, especially around the midsection.
- A person having a theoretical body type with slow metabolism in which weight is gained easily, but fat levels are hard to reduce. Endomorphic bodybuilders tend to be the most massive.