At restaurants nowadays all over the world, sit-in or fast-food, most
offer free refills on drinks. Just who started this practice and how
did it result in this trend?

No answer from me, but I would like to add that free drink refills are
virtually unknown in Germany. Actually, they are widely considered a
"typical American deplorable custom".

Greetings,
Scriptor

I first remember Carl's Jr. causing a stir in the fast food industry
with free drink refills.  When they charge about a dollar for a small
soda that only costs them a few cents, I think the term "free" is
misleading. You would have to drink a lot of soda to wipe out their
profit margin.  Also, many people don't get refills or only one to go.
 As far as a previous comment saying it is a typical deplorable
American custom is concerned, it is sour European grapes.