The concept that mass increases with speed is derived from Einstein's theory of special relativity. According to this theory, as an object's velocity approaches the speed of light, its mass appears to increase.
However, it's important to note that this increase in mass is a relativistic effect and is not directly observed in the object's rest frame. From the object's perspective, its mass remains constant regardless of its speed.
On the other hand, weight is a measure of the force exerted on an object due to gravity. It is dependent on the mass of the object and the gravitational field strength. Weight is given by the formula:
Weight = Mass * Acceleration due to gravity
Since the gravitational field strength near the Earth's surface remains relatively constant, the weight of an object doesn't change significantly with changes in speed. The weight is determined by the object's mass and the acceleration due to gravity, both of which remain constant in this scenario.
So, while the concept of mass increase with speed is part of the theory of special relativity, it doesn't directly affect the weight of an object as weight is determined by the object's mass and the gravitational field strength.