The most common and most likely answer to this crossword clue is the 10 plus 5 letter word WEDNESDAYS CHILD
I've seen this crossword clue in The Guardian
W
E
D
N
E
S
D
A
Y
S
C
H
I
L
D
More clues leading to the result WEDNESDAYS CHILD
Buddy explains!
The straight part
We know that "Weekly issue full of woe" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weekly issue full of woe = wednesdays child.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.