The most common and most likely answer to this crossword clue is the 7 plus 5 letter word CUSTARD TARTS
I've seen this crossword clue in The Daily Telegraph
C
U
S
T
A
R
D
T
A
R
T
S
More clues leading to the result CUSTARD TARTS
Buddy explains!

The straight part
We know that "Sweet things" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sweet things = custard tarts.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.