What is the origin of “heart goes out to”?

The earliest reference I can find is from the 1754 book Historical Collections Relating to Remarkable Periods of the Success of the Gospel, and is from "From Mr. Edwards' Sermon at Mr. Brainerd's Funeral" that took place in 1746. In this part, Jonathan Edwards is quoting David Brainerd:

My heart goes out to the burying-place, it seems to me a desirable place : but O to glorify God ! That is it ! that is above all !

This was also published in at least two other 19th century books. Other than that, here are the three other 19th century references.

From Faithful contendings displayed: being an historical relation of the state ... By John Howie, here's "Sermon II. Galations V. I." by Mr. John Kid:

It is a wonder to me, that some are in their right- minds, and not breaking their very hearts for his return. What do ye say ? Tell him from me, my heart is with him. My soul is with him : my heart goes out after him ; and I am sick with love.

1784's Diary and Letters of Madame D'Arblay: 1778 to 1784 By Fanny Burney, in a 1779 diary entry:

And now let me stop this conversation, to go back to a similar one with Dr. Johnson, who, a few days since, when Mrs. Thrale was singing our father's praise, used this expression :
"I love Burney : my heart goes out to meet him !"
" He is not ungrateful, sir," cried I ; " for most heartily does he love you."

1786's Journal of Rev. Francis Asbury: bishop of the Methodist Episcopal ...: Volume 1, from the entry for Friday 10th November 1775:

I have now a blooming prospect of usefulness, and hope both to do good and get good. My heart goes out in grateful thanksgiving and praises to God.