You were quite close, but it's not 한폄 (no such word) but 한 뼘, that is, "a handspan".
He actually says 한 뻠은 더 커서 그래. 은 here adds a little emphasis but also makes the sentence flow better.
뼘 means the width of the hand when fully stretched out, from the tip of the thumb to the tip of the little finger.
It often means a small distance or gap rather than the actual length, as used in this example.
Children like to use this word a lot in their play, like 한 뼘, 두 뼘, 세 뼘, etc.
By the way, it's 김복주, not 김북주. "북" is almost never used in people's names :-)