"grows large" is correct and usable in written English.
You can use it when describing something that increases in size. For example, "The tree grows larger every day."
The sky grows dark; the sun grows large, red, and dim.
If it grows large enough, the BBC will have a hard time justifying the licence fee.
Because it is fattened, it grows large, about twice the size of a Pekin.
But if the anger against Wall Street grows large enough, that could change.
Sometimes his nose grows large, possibly when he's lying to himself.
When the shrub grows large and woody, it can practically steal your date at a party.
When the bubble grows large enough, it will departure quickly under the force of channel pressure.
Ideally, all this happens before the problem grows large enough to harm employees, customers, or other stakeholders.
As the twin grows large enough, however, elastic interactions and displacive character of the transformation should always turn dominant.
In heart failure, the heart can no longer pump efficiently and grows large in a futile attempt to overcome the problem.
The box elder (Acer negundo) has very good resistance and offers lovely autumn colour, though it grows large – 12 metres tall after 20 years.
