Well, we can agree that the answer is context-dependent.
In the context of the most-naive students, there are a hundred good
reasons for not mentioning "gravity" at all ... not until they have
some clue what is a "force" and what is an "acceleration".
Gravity is not a good introductory example of force /or/ acceleration.
If the gravity question comes up, you can either duck the question
entirely, or explain it a little bit (with the expectation that they
won't 'get' it, and you'll have to explain it again later).
Some texts provide a systematic introduction to the notion of force,
and some don't. If your text jumps right in, using weight as "the"
canonical example of a force, then you've been painted into a corner.