The most common and most likely answer to this crossword clue is the 11 letter word AVOIRDUPOIS
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More clues leading to the result AVOIRDUPOIS
Buddy explains!

The straight part
We know that "weight perhaps" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weight perhaps = avoirdupois.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 AVOIRDUPOIS mean?
AVOIRDUPOIS noun- The official system of weights used in the UK between 1856 and 1963. It had been the customary system in London since 1300.
- The official system of weights used in the USA between 1866 and 1959.
- Weight; heaviness (commonly with humorous intent).