The most common and most likely answer to this crossword clue is the 10 letter word BALLOONING
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Buddy explains!

The straight part
We know that "double defn." is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case double defn. = ballooning.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 BALLOONING mean?
BALLOONING verb- To increase or expand rapidly.
- To go up or voyage in a balloon.
- To take up in, or as if in, a balloon.
- To inflate like a balloon.
- To strike (a ball) so that it flies high in the air.
- The act of something that swells or expands.
- The sport or hobby of flying in a balloon.
- The mechanical kiting used by spiders, mites, caterpillars, etc. to travel through the air.
- Growing rapidly as a balloon.
- Rising high in the air.