your weight is just your normal force!

Intro physics textbooks often jump over backwards to deal with the problem that astronauts (say) feel weightless, but in fact they are subject to a gravitational force that is only a few percent less than the gravitational force here on Earth. And then there is all the discussion of why they feel weightless when in fact they have nearly the same weights as we do.

I simply don't agree with this: In my view, your weight is your normal force against the floor when you are in static equilibrium in your local rest frame. Here are some arguments for my position:

the gravitational force is unobservable:
It is literally a constituent principle of modern physics that you can't tell a gravitational force from a non-gravitational force in an accelerated reference frame. So if we decide that “weight” is gravitational force, we have decided that weight is completely unobservable. So, presumably, everyone is wrong about their weight, and their weight is actually not a covariant property of anything.
everyone becomes right:
In the standard textbook view, astronauts are misguided about their weightlessness, as are passengers on the vomit comet. We have to say they “feel” weightless but aren't. Also, we have to say that people on a roller coaster who go over hills and valleys feel lighter and heavier, but when in fact (we have to say) actually nothing has changed. In my new view, the astronauts, passengers, and ride-goers are all correct: They really are weightless (in the space station and the comet), and they really are changing their weight (on the roller coaster) as they ride.
museum exhibits don't have to change:
It is still the case that you are heavier on Jupiter (if it had a surface) and lighter on Mars! Because the normal force you would feel would be higher and lower. Totally observable, totally true.
buoyancy gets taken care of naturally:
What does a helium balloon weigh? In the standard gravitational-force sense, something positive. But in the normal-force sense something negative! It has to be tied down to the floor. That seems sensible. Also, even humans have a buoyant force acting on them, it decreases their weight (in my view, but not in the standard view). Like should a doctor's office multiply everyone's weight measurement by (1+1/800) to account for buoyant force? They should if weight is weight is gravitational force, but not if weight is normal force. Again, this also connects to observability, and also the correctness of visceral feelings (like your feeling of weightlessness in a swimming pool). [Modification made later: Will Kinney (SUNY Buffalo) makes a great point: Your inner ear feels the normal force you would have with no abnormal buoyant force, whereas your feet on the floor feel a normal force that is modified if you are in a denser medium, so the buoyancy point here is complex to say the least.]
it disambiguates weight from mass better:
Mass is a gravitational charge, or an inertial constant. Weight is a force. If weight is going to be a force, it should be an observable, measurable force. Preferably the force you actually feel when you say “I feel heavy”. So make weight the observable force, and mass something to be inferred by inertial and gravitational arguments.

The funny thing about all these changes is that they change nothing in natural language or natural discussion of weight, and they greatly simplify physical discussions of weight. They also make it less true that physics is in Physics Land (tm) where all your intuitions are wrong! I hate Physics Land (tm) and this redefinition of the word weight tears down one of its (many, many) walls.