The most common and most likely answer to this crossword clue is the 4 letter word MNAS
M
N
A
S
Buddy explains!

The straight part
We know that "Weight used by Greeks" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weight used by greeks = mnas.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 MNAS mean?
MNAS noun- A monetary unit of ancient Greece and the Middle East, originally equivalent to the weight of a mina of silver.
- A unit of weight of varying value used in the ancient Middle East, especially Babylonia, Mesopotamia and Egypt; also an ancient Greek measure of weight equivalent to 1/60th of a talent.
- One of the South and East Asian birds of the starling family Sturnidae.