The most common and most likely answer to this crossword clue is the 7 letter word REFRAIN
I've seen this crossword clue in The Times
R
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More clues leading to the result REFRAIN
Buddy explains!

The straight part
We know that "Burden" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case burden = refrain.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 REFRAIN mean?
REFRAIN verb- To hold back, to restrain (someone or something).
- To show restraint; to hold oneself back.
- To repress (a desire, emotion etc.); to check or curb.
- (with preposition "from") To stop oneself from some action or interference; to abstain.
- To abstain from (food or drink).
- The chorus or burden of a song repeated at the end of each verse or stanza.
- A much repeated comment, complaint, or saying.