"Friday Evening.I had your letter late last night, everyone almost, being out of the house by an accident, so that it was left in the letter-box, and if I had wished to answer it before I saw you, it had scarcely been possible.
But it will be the same thing—for you know as well as if you saw my answer, what it must be, what it cannot choose but be, on pain of sinking me so infinitely below not merely your level but my own, that the depth cannot bear a glance down. Yet, though I am not made of such clay as to admit of my taking a base advantage of certain noble extravagances, (and that I am not I thank God for your sake) I will say, I must say, that your words in this letter have done me good and made me happy, ... that I thank and bless you for them, ... and that to receive such a proof of attachment from you, not only overpowers every present evil, but seems to me a full and abundant amends for the merely personal sufferings of my whole life. When I had read that letter last night I did think so. I looked round and round for the small bitternesses which for several days had been bitter to me, and I could not find one of them. The tear-marks went away in the moisture of new, happy tears. Why, how else could I have felt? how else do you think I could? How would any woman have felt ... who could feel at all ... hearing such words said (though 'in a dream' indeed) by such a speaker?"
She is not referring to Browning's analysis of her duty to herself regarding going to Italy. She is specifically referring to Browning's saying that if he could life his dream he would immediately marry her.
"And now listen to me in turn. You have touched me more profoundly than I thought even you could have touched me—my heart was full when you came here to-day. Henceforward I am yours for everything but to do you harm—and I am yours too much, in my heart, ever to consent to do you harm in that way. If I could consent to do it, not only should I be less loyal ... but in one sense, less yours. I say this to you without drawback and reserve, because it is all I am able to say, and perhaps all I shall be able to say. However this may be, a promise goes to you in it that none, except God and your will, shall interpose between you and me, ... I mean, that if He should free me within a moderate time from the trailing chain of this weakness, I will then be to you whatever at that hour you shall choose ... whether friend or more than friend ... a friend to the last in any case. So it rests with God and with you—only in the meanwhile you are most absolutely free ... 'unentangled' (as they call it) by the breadth of a thread—and if I did not know that you considered yourself so, I would not see you any more, let the effort cost me what it might. You may force me feel: ... but you cannot force me to think contrary to my first thought ... that it were better for you to forget me at once in one relation. And if better for you, can it be bad for me? which flings me down on the stone-pavement of the logicians.
And now if I ask a boon of you, will you forget afterwards that it ever was asked? I have hesitated a great deal; but my face is down on the stone-pavement—no—I will not ask to-day—It shall be for another day—and may God bless you on this and on those that come after, my dearest friend."
So, he finally 'forced' it out of her. But she has put a big condition on it. She does not say that she will marry him. As carefully as she makes it clear that he is 'unentangled' she also makes it perfectly clear that she is free as well. She will not marry him if her health does not improve. Browning wastes no time in responding:
"Think for me, speak for me, my dearest, my own! You that are all great-heartedness and generosity, do that one more generous thing? God bless you for R.B.
What can it be you ask of me!—'a boon'—once my answer to that had been the plain one—but now ... when I have better experience of—No, now I have best experience of how you understand my interests; that at last we both know what is my true good—so ask, ask! My own, now! For there it is!—oh, do not fear I am 'entangled'—my crown is loose on my head, not nailed there—my pearl lies in my hand—I may return it to the sea, if I will!
What is it you ask of me, this first asking?"
His response will be a recurring theme with him: he wants her to be in charge of him, "Think for me, speak for me," he asks her now and late in their courtship he describes how he wants her to 'drive' and make the decisions for them both. She says she is, "yours for everything but to do you harm," and he seems quite delighted with the notion that she is "my own". The "boon" she is referring to is (will you be disappointed if I tell you now and don't make you wait for it, my little blogoleers? I am going to tell you anyway. You are warned, close your eyes if you don't want to know) the missing letter that he sent after their first meeting. She told him to burn it. She is assuming that he did not burn it. He certainly is eager to fulfill her request.