How does the weight of an object vary with respect to mass and radius of earth? In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its presents value, then how would the weight of any object on the surface of the earth be affected?

Weight of an object is directly proportional to the mass of earth and inversely proportional to the square of the radius of the earth. i.e.,

Weight of a body ∝ {M \over R^2}

Original weight, W₀ = mg = m G {M \over R^2}

When hypothetically M becomes 4 M and R becomes {𝑅 \over 2}

Then weight becomes W_{n = m G {4M \over ({R \over 2})^2} = (16 m G){M \over R^2} = 16 x W0}

The weight will become 16 times.