bigger growth

[Dr.Appalayya]

In four months after its birth, the puppy has grown bigger in size.

I want a correct adjective for such (bigger, higher, heavier) growth.

[banderas]

In four months after its birth, the puppy has grown bigger in size.

I want a correct adjective for such (bigger, higher, heavier) growth.

We do not need any adjective in "grow in size". It is a good idea to express it using a verb "grow" and one of the adverbs.
The puppy quickly grew into a large dog.

Commonly used adverbs: (grow) fast, quickly, rapidly, slowly, steadily, exponentially.

[Dr.Appalayya]

Can I call it 'bigger growth or higher growth?

[banderas]

Can I call it 'bigger growth or higher growth?

I' ve never heard of bigger growth.
Higher growth works pretty well in the sentence like this:

"On the economic side it was believed that customs union, by creating healthy competition and allowing for large-scale production, would have a dynamic effect, leading to higher growth and better living standards."

[RonBee]

In four months after its birth, the puppy has grown bigger in size.

In the four months since its birth the puppy has grown larger.