Would you weigh more or less on the Moon, and why?

Answer

You would weigh less on the Moon because the Moon’s gravitational field is weaker than Earth’s. Weight is the force of gravity on your mass, $W = mg$, and the Moon’s $g$ is about $1.62\,\text{m/s}^2$ compared with Earth’s $9.8\,\text{m/s}^2$. That means you would weigh about $1/6$ as much on the Moon, even though your mass stays the same.

Explanation

What the question is really asking

This is about the difference between mass and weight. Your mass is how much matter you have, but your weight depends on how strongly gravity pulls on that mass.

Using the weight equation

Weight is given by

$$W = mg$$

where $m$ is your mass and $g$ is the local gravitational acceleration.

Comparing Earth and Moon gravity

Earth: $g \approx 9.8\,\text{m/s}^2$
Moon: $g \approx 1.62\,\text{m/s}^2$

So the ratio is

$$\frac{W_{\text{Moon}}}{W_{\text{Earth}}} = \frac{g_{\text{Moon}}}{g_{\text{Earth}}} \approx \frac{1.62}{9.8} \approx 0.165$$

That is close to $1/6$.

What stays the same

Your mass $m$ does not change when you go to the Moon. Only $g$ changes, so your weight changes.

Quick example

If you weigh $600\,\text{N}$ on Earth, then on the Moon you would weigh about

$$600\,\text{N} \times 0.165 \approx 99\,\text{N}$$

So you weigh much less on the Moon.