Which word would best describe a request made with earnestness?

The term that best describes a request made with earnestness is "plea." A plea is an earnest and emotional appeal or request for help or support, often made in a sincere, heartfelt manner. It conveys urgency and a deep desire for something to be granted or understood, which aligns closely with the concept of making a request earnestly.

In contrast, the other words do not reflect the same sense of earnestness or sincerity. "Plummet" refers to a rapid decline or fall and does not relate to the nature of a request. "Pompous" describes something characterized by an exaggerated sense of self-importance or arrogance, which is quite contrary to the nature of an earnest request. Lastly, "pine" means to long for something or to feel a deep sadness, which while it can imply a strong feeling, does not specifically denote making a request. Thus, "plea" is the word that most accurately captures the essence of an earnest request.