Well, the bare-bones explanation is that if another creature is going to take on Godzilla, it needs to be equal in strength and power. And since Kong doesn't fly, he needs to get sized-up considerably in order to square off against "The Zill."
In the context of the fictional universe of the "MonsterVerse" films, Kong's accelerated growth rate can be attributed to the unique ecosystem of Skull Island, where he originates. The island's environment and resources may have contributed to Kong's rapid growth and larger-than-average size compared to other kaiju.