Step 1: Newton's law of universal gravitation gives the attractive force between the Earth, mass \( M \), and a body of mass \( m \) at distance \( R \) from Earth's centre as: \[ F = \frac{GMm}{R^2} \]
Step 2: Near the Earth's surface, \( R \) is essentially constant, Earth's radius, so the quantity \( \frac{GM}{R^2} \) is itself a constant. This constant is defined as the acceleration due to gravity, \( g = \frac{GM}{R^2} \).
Step 3: Substituting this back into the force expression gives \( F = mg \), a force that always points toward the Earth's centre, this specific gravitational force is what is called the weight of the body. \[ \boxed{\text{Weight } = mg} \]