The Moon's gravity is 1/6 of the Earth's gravity. The weight of a bowling ball on the Earth would be 6 times its weight on the Moon.The gravity on the surface of a body depends on its mass.
Newton’s law of gravitation is
$F = \frac{G m_1 m_2 }{ r^2}$
F = force of gravity on the thing being weighed, i.e. it’s weight
G = Gravitational constant
$m_1$ = first mass, or mass of the planet
$m_2$ = second mass, mass of the thing being weighed on the planet
r = distance between the centers of mass of the two objects, which in this case is just the radius of the planet.
$g = \frac{G m_1 }{ r^2}$
Then your weight is
$F = g m^2$
The ratio of gravity on the moon to the gravity on earth is then
$R = \frac{g(moon)}{g(earth)}$
$R = \frac{( G m(moon) / r(moon)^2)} {( G m(earth) / r(earth)^2 )}$
If you simplify this and plug in the radii of the earth and moon, you do get ⅙.
Hence he weight of a bowling ball on the Earth would be 6 times its weight on the Moon.