The most common and most likely answer to this crossword clue is the 6 letter word WAXING
I've seen this crossword clue in The Guardian
W
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More clues leading to the result WAXING
Buddy explains!

The straight part
We know that "growing bigger" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case growing bigger = waxing.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 WAXING mean?
WAXING verb- To apply wax to (something, such as a shoe, a floor, a car, or an apple), usually to make it shiny.
- To remove hair at the roots from (a part of the body) by coating the skin with a film of wax that is then pulled away sharply.
- To defeat utterly.
- To kill, especially to murder a person.
- (usually of a musical or oral performance) To record.
- To increasingly assume the specified characteristic.
- To grow.
- (of the moon) To appear larger each night as a progression from a new moon to a full moon.
- (of the tide) To move from low tide to high tide.
- The action of the verb to wax.
- A cosmetic procedure in which hair is removed from the body by the application and removal of wax.
- A recording intended for a phonograph.