The phrase "vast preponderance" means that there is a significantly larger amount or majority of something compared to the opposing side. Full definition
Before the past two decades, the vast preponderance of Christian writers on sexuality assumed that the question before them was simply: What does Christianity (the Bible, the tradition, ecclesiastical authority, etc.) say about sexuality? (religion-online.org)
But the vast preponderance of governing power belongs within the free nations of the world community, and not to any world body. (religion-online.org)