The most common and most likely answer to this crossword clue is the 7 letter word IMPOSED
I've seen this crossword clue in The Daily Telegraph
I
M
P
O
S
E
D
Buddy explains!

The straight part
We know that "Burdened" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case burdened = imposed.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 IMPOSED mean?
IMPOSED verb- To establish or apply by authority.
- To be an inconvenience (on or upon)
- To enforce: compel to behave in a certain way
- To practice a trick or deception (on or upon).
- To lay on, as the hands, in the religious rites of confirmation and ordination.
- To arrange in proper order on a table of stone or metal and lock up in a chase for printing; said of columns or pages of type, forms, etc.