The most common and most likely answer to this crossword clue is the 5 letter word TUMID
I've seen this crossword clue in The Guardian
T
U
M
I
D
More clues leading to the result TUMID
- Little girl’s back and stomach on front, swollen
- Puffed up Dublin parliamentarian adopts superior note
- Bloated stomach, wind periodically expelled
- Swollen stomach: girl’s knocked up
- Swollen belly and oddly windy
- Bombastic leaders of trade union, stupid on reflection
- Starts treating underage mother — identifies diaphragm being swollen
- Corporation documents, puffed up
Buddy explains!

The straight part
We know that "puffed up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case puffed up = tumid.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 TUMID mean?
TUMID adjective- Swollen, enlarged, bulging
- Cancerous, unhealthy
- Pompous, bombastic