Both Uses

oblige
in
Through the Looking-Glass
(Edited)

There was a Beetle sitting next to the Goat (it was a very queer carriage-full of passengers altogether), and, as the rule seemed to be that they should all speak in turn, HE went on with 'She'll have to go back from here as luggage!'
Alice couldn't see who was sitting beyond the Beetle, but a hoarse voice spoke next. 'Change engines--' it said, and was obliged to leave off.
Chpt 3 *

obliged = required (to do something)
So much obliged!
Chpt 4 *

obliged = grateful or indebted

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.