Explain whether body weight depends on the conditions of its movement.

No, it doesn’t. Body weight is the force with which the body acts on the support. Regardless of the movement, this force does not change, because the body’s mass does not change.
Body weight is the product of mass and gravitational acceleration.
P = mg
So, regardless of the speed and other values, the weight of the body does not change while the body is on the support. Of course, if the body is in the air, then it is in a state of weightlessness, because there is no support reaction.