I was reading Mauritius Command by Patrick O'Brian and I came across the following:

page 41...

"Why, he has lost a great deal of blood, it cannot be denied; but then on the other hand I have rarely seen a man with so much blood to lose. He should do very well, with the blessing.

page 104...

"I call at the second house I see...I make a contact of inestimable value, receive my information, deliver these documents, whose extreme tenuity, you see...renders them edible, ...I walk back to the boat..to join you, with the blessing, for breakfast."

and page 273...

"Now, sir," said Stephen, standing up,"I must beg to take my leave: the boat is no doubt waiting, and I shall have harsh words if I do not hurry."
"I shall see you again very shortly?" asked Farquhar.
"Yes, with the blessing."

I couldn't figure out blessing in these contexts, but then I remembered this from Bobbie Burns:

I doubt na, whyles, but thou may thieve;
What then? poor beastie, thou maun live!
A daimen icker in a thrave
'S a sma' request.
I'll get a blessin wi' the lave,
An never miss't!

There seems, to me, to be a vague parallel between Burns's usage and O'Brian's. Something to do with "left-overs" or "remainders". Burns uses lave which means "what's left" and O'Brian, at least on page 41, seems to refer to the patient's reserve of blood.


Is this an obsolete use for blessing? All these references are historical or historical fiction.

Well, I can tell you that in all those contexts I could see the Jewish use of blessing working. Jews have blessings (prayers) for a number of different activities. For example, in the first, he should do very well, as long as you pray for him (a blessing). In the second he is joining for both prayer (blessing) and breakfast. In the next, he could be referring to the travel blessing.

I don't know, though. Obviously these aren't Jewish authors. Would other religions use it this way?

Maybe the usage here is some sort of shorthand for "with God's blessing" or "if God wills". Those phrases could all be substituted for "blessing" and still make sense; although it might not be the right sense!