The most common and most likely answer to this crossword clue is the 8 letter word GRAVITAS
I've seen this crossword clue in Independent
G
R
A
V
I
T
A
S
More clues leading to the result GRAVITAS
- Importance of life in lawn area that’s been cut
- Importance one attached to reducing sauce, tasted halfway through
- Life in rags changed, gaining importance
- Dignity — informer briefly clutches Bible with it
- Good Indian dish carrying very small weight
- Importance of a vast rig at sea
- Weight of a vast rig collapsing
- Weight of importance? No end, since eating Italian
- Iceland receives acknowledgement after sauce reduced weight
- Importance of last king taking on a mission to get rid of king
Buddy explains!

The straight part
We know that "weight" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weight = gravitas.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 GRAVITAS mean?
GRAVITAS noun- Seriousness in bearing or manner; dignity
- Substance, weight