"grows larger" is correct and usable in written English.
You can use it to describe the increasing size of something over time. For example, "The population of the city grows larger every year."
Instead, that which remains behind grows larger.
With Slingshot, Facebook's portfolio of apps grows larger still.
The handkerchief flutters, grows larger, and suddenly splits in half.
The electrochemical catalyst activities weaken as the diameter grows larger.
As the show grows larger, its theme packs a bigger cultural punch.
Then they frolic together, joining a multinational playgroup that grows larger as the book goes on.
A cavity in the ground grows larger and larger, then, basically, it migrates to the surface".
As Amy's story develops, so the audience watching her grows larger.
Across the river is Lou Lamoriello, whose shadow only grows larger.
As the minority population grows larger, who is being turned away from certain public schools?
A vehicle's (velocity) fluctuation grows larger and it neglects keeping the homogeneous movement of grouping vehicles.
