I still see both definitions in common practice in
high school, first year physics texts and in
engineering texts. So, apparently neither has been
abandoned yet. Please let me know when you have
convinced the authors of these texts to change their
definitions.
Defining weight as mg and mMG/r^2 is common practice
in high school and first year college level physics
texts.
But since g is not the same as MG/r^2 on the surface
of the Earth, it would seem that at least one of these
"definitions" would have to be abandoned. I'd suggest
that if you do keep one of them, it should be the
first one.