All 6 Uses

oblige
in
Cold Sassy Tree
(Edited)

I'm much obliged.

obliged = grateful or indebted
Shouting above the train noise, I told him much obliged for saving T.R.
When Mr. Beach offered to carry me home in his buggy, I said, "Thank you, sir, I'd sure be much obliged."
*
Then as he pulled up his suspenders, he said, real formal, "I'm much obliged to you, Miz Rucker Blakeslee."
I respect yore position in the Presbytery, Hoyt, but I'd be much obliged if will Tweedy could leave early to drive us.
We're much obliged, but Miss Mattie Lou don't need no more hep.

Definitions:

(1) (oblige as in: I am obliged by law.)
require (obligate) to do something
(2) (oblige as in: I obliged her every request.)
grant a favor to someone
(3) (obliged as in: I'm much obliged for your kindness)
grateful or indebted
(4) (meaning too rare to warrant focus)
Much more rarely, in classic literature you may see oblige as a synonym for ask as when Jules Verne wrote "I obliged the Professor to move his lamp over the walls of the gallery," in Journey to the Center of the Earth.