If something is preponderant, it is the main one — the largest share, the most common, or the one that carries the most weight in a group. A preponderant view is the view most people hold. A preponderant majority is a majority so large it outweighs the rest. It is a formal, almost school-essay word. You meet it in careful writing and news analysis; everyday English says main, the biggest, or the most common. The picture behind it is a pair of scales: this side outweighs the other. Though actually, it does not always mean most important in a moral sense — it often just means the bigger pile. The noun people use even more is preponderance: the preponderance of evidence. There is a rare verb, preponderate, “to outweigh,” but students almost never need it.