The most common and most likely answer to this crossword clue is the 9 letter word MILLSTONE
I've seen this crossword clue in The Daily Telegraph
M
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More clues leading to the result MILLSTONE
- Mass troubles to Tyneside perhaps can be a burden
- Some returning Huguenots'll import a heavy burden
- Philosopher’s temper becomes a cross to bear
- Philosopher’s style becoming a bugbear
- Philosopher’s style is something hard to bear
- Omen still represented heavy burden
- Learners caught in fine rain with one load hard to bear
- Philosopher’s vocal character proving a heavy burden
- Thousand still confused before somebody has burdensome responsibility
Buddy explains!

The straight part
We know that "heavy burden" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case heavy burden = millstone.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 MILLSTONE mean?
MILLSTONE noun- A large round stone used for grinding grain.
- A coarse-grained sandstone used for making such stones; millstone grit.
- Often in a millstone round one's neck (referring to Matthew 18:6 in the Bible): a heavy responsibility that is difficult to bear.