There's plenty gravity on the moon.
The acceleration (strength) of gravity on the surface of any
planet, moon, asteroid, comet, etc. depends on the mass
and size of that body.
The Moon's mass is about 1/80 as much as the Earth's mass,
and its diameter is about 0.273 the size of Earth's diameter.
(about 1/80) times (about 1/0.273²) = about 0.168
This says that the Moon's gravity should be about 0.168
as strong as the Earth's gravity.
The real number is 0.165 . Not bad.