The most common and most likely answer to this crossword clue is the 12 letter word OVERBURDENED
I've seen this crossword clue in The Guardian
O
V
E
R
B
U
R
D
E
N
E
D
Buddy explains!

The straight part
We know that "Weighed down" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weighed down = overburdened.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 OVERBURDENED mean?
OVERBURDENED verb- To overload or overtax
- Excessively burdened