The most common and most likely answer to this crossword clue is the 8 letter word PORTLIER
I've seen this crossword clue in The Times
P
O
R
T
L
I
E
R
Buddy explains!

The straight part
We know that "more stout" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case more stout = portlier.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 PORTLIER mean?
PORTLIER adjective- Somewhat fat, pudgy, overweight.
- Having a dignified bearing; handsome, imposing.