I agree with much that has already been said. I also think that the letter contains elements of what Willoughby has said to Sophia about the Dashwood ladies and his time in Devonshire. Here is a possible scenario:-

Sophia has just read Marianne's letter, the rumours of a girl in Devonshire are true after all. She is very upset ("her tears"), but more to the point she is righteously angry, furious, in an absolute passion, and she lets it show!

Willoughby is given his marching orders....

He protests, he pleads - "I beg you - don't throw away our love. Please - give me a chance - I can explain!!"

After a good deal of this sort of thing Sophia relents a little and consents to hear his explanation, but it had better be good! She is simmering....

Willoughby takes the floor and uses every means in his power to win her over. He tells her of the new family who had come to live in a cottage near Allenham.

W: “You know how it is in the narrow confines of country society - one is grateful for any new faces to vary the scene. The mother in particular a most agreeable woman - respectable - very hospitable - intelligent. She had us all reading Shakespeare together - hardly my usual style, I'll grant you, but it made a welcome change from the sort of gossip and meaningless nothings one usually has to endure.
I spent some very pleasant evenings with them all, and came to like the family as a whole very well – perhaps I was too unguarded in my professions of that esteem, and must have been misunderstood.
Miss Marianne? Rather gauche, just out of the schoolroom I suppose, still learning how to conduct herself in good society. Endlessly chattering - all I could do to get a word in edgeways. Trying to prove herself as well-read as her mother and elder sister I imagine. No wit, no style. Not at all the sort I could ever think remotely attractive.
I suppose she must have felt it was time she had a little tendre for someone, and I would do as well as anyone. I had no notion of it until I was leaving and she gave me a lock of her hair wrapped in a piece of paper. I could scarcely refuse to take it, so I just put it in my pocket book and thought no more about it. All I could think of was that at last I was coming back to you my darling...
Until last night I had not seen them since I left Devonshire. I was horrified when I received her notes - certainly had no thought of answering them - that would only have encouraged her. - with our engagement still a secret I could not explain why she should not think of me as anything more than a friend of the family.
Impossible that that I had any particular feelings for her - you must know my whole heart has long been devoted only to you and you alone."
(Insert here any amount of cajolery, flattery and protestations of Sophia's many perfections. Willoughby has had a lot of practice at this sort of thing, and with £50,000 at stake I'm sure he was giving it his all at this point.)

Sophia begins to be convinced, but she insists that he return the letters and the lock of hair.

W: “I'll do it today.”

S: “You will do it now, before you leave this house, or our engagement is at an end. Do I make myself clear? Here is a pen and paper....”

W: (whining) “But what can I say?”

S: “I fail to see the difficulty. You have just explained everything to me quite clearly.”

Willoughby attempts to write the letter - crumples up his first attempt. He sighs, looks winsome, & says ruefully "I don't know how to say what must be said without giving offence - I can't seem to find the right form of words to begin..."

S: (exasperated) "Oh for goodness sake! Let me try..." (She drafts the letter.)
S: “There you are - nothing could be simpler. See, it is perfectly courteous. I have even cast it in a fine manly style for you.”

W: cravenly copies the letter..... and the rest is history.