Q.Define weight.

Weight versus gravitational force. The gravitational force on a mass $m$ is always $mg$, pointing straight down. Weight, though, is formally defined as the magnitude of the upward force needed to hold the object at rest (or constant velocity) -- ordinarily, this is just the normal reaction force from whatever surface supports the object, so $W=N=mg$ when nothing is accelerating. They agree numerically at rest, but conceptually they are different quantities: weight is about the support force, not the gravitational pull itself.

Apparent weight in an accelerating lift. Applying Newton's second law to a person of mass $m$ standing on a scale in a lift gives:

• At rest / constant velocity: $N=mg$ -- apparent weight equals true weight.
• Accelerating upward (acceleration $a$): $N=m(g+a)$ -- apparent weight is greater than $mg$ (the "heavy" feeling as a lift starts going up).
• Accelerating downward (acceleration $a$): $N=m(g-a)$ -- apparent weight is less than $mg$ (the "light" feeling as a lift starts going down).
• Free fall ($a=g$, e.g. cable cut): $N=m(g-g)=0$. The scale reads exactly zero -- this is weightlessness. …