Zero-g
Weightlessness, or an absence of 'weight', is an absence of stress and strain resulting from externally applied mechanical contact-forces, typically normal forces from floors, seats, beds, scales, and the like. Counterintuitively, a uniform gravitational field does not by itself cause stress or strain, and a body in free fall in such an environment experiences no g-force acceleration and feels weightless. This is also termed "zero-g" where the term is more correctly understood as meaning "zero g-force."
When bodies are acted upon by non-gravitational forces, as in a centrifuge, a rotating space station, or within a space ship with rockets firing, a sensation of weight is produced, as the contact forces from the moving structure act to overcome the body's inertia. In such cases, a sensation of weight, in the sense of a state of stress can occur, even if the gravitational field were zero. In such cases, g-forces are felt, and bodies are not weightless.
When the gravitational field is non-uniform, a body in free fall suffers tidal effects and is not stress-free. Near a black hole, such tidal effects can be very strong. In the case of the Earth, the effects are minor, especially on objects of relatively small dimension (such as the human body or a spacecraft) and the overall sensation of weightlessness in these cases is preserved. This condition is known as microgravity and it prevails in orbiting spacecraft.
In October 2015, the NASA Office of Inspector General issued a health hazards report related to human spaceflight, including a human mission to Mars.
In Newtonian mechanics the term "weight" is given two distinct interpretations by engineers.
To sum up, we have two notions of weight of which weight1 is dominant. Yet 'weightlessness' is typically exemplified not by absence of weight1 but by the absence of stress associated with weight2. This is the intended sense of weightlessness in what follows below.
A body is stress free, exerts zero weight2, when the only force acting on it is weight1 as when in free fall in a uniform gravitational field. Without subscripts, one ends up with the odd-sounding conclusion that a body is weightless when the only force acting on it is its weight.
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