Answer
One-half the astronaut's weight on Earth.
Work Step by Step
$$Weight_{on Earth}= G \frac{M_{Earth} m}{(d_{Earth})^{2}}$$
$$Weight_{new \;planet}= G \frac{2 M_{Earth} m}{(2 d_{Earth})^{2}} = \frac{1}{2} \times Weight_{on Earth}$$
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