The most common and most likely answer to this crossword clue is the 9 letter word NONENTITY
I've seen this crossword clue in Financial Times
N
O
N
E
N
T
I
T
Y
More clues leading to the result NONENTITY
- One idiot, about time, breaking city cipher
- Tinny tone upset nobody
- Intent on working out Bletchley's last cipher
- Loser in nine-piece muffling note encountering enmity? Not half
- Not one idiot in US city is a lightweight
- Ninety ton, miserable lightweight!
- Nobody not ninety is dancing
- Nobody in yet? Not unusual around noon
- What could be 90-ton lightweight
- Nobody of note, tiny person ultimately? Possibly
Buddy explains!

The straight part
We know that "a lightweight" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a lightweight = nonentity.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 NONENTITY mean?
NONENTITY noun- An unimportant or insignificant person
- : the state of not existing; nonexistence