Weight is a measure of the force of gravity acting on an object. The force of gravity is directly proportional to the mass of the object and inversely proportional to the square of the distance from the center of the object.

In this case, the planet has the same mass as Earth, but twice the diameter. This means that the distance from the center of the planet to the surface is twice as great as it is on Earth. Therefore, the force of gravity on the planet is 1/4 of the force of gravity on Earth.

Since weight is directly proportional to the force of gravity, this means that the astronaut's weight on the planet would be 1/4 of their weight on Earth.