We all know that on the moon, you weigh about 1/6 what you weigh on Earth. And we’ve all seen pictures of the lunar astronauts bounding around in semi-weightlessness, as if everything were in slow-motion.
I don’t get it. Suppose there’s a 200-lb. man on the moon, and a 33-lb. kid on earth. They both might “weigh” the same, but the man appears to be leaping around in slow-motion, and the kid moves normally. So what else is a factor here, besides gravity?
Because of the lower gravity the acceleration of objects (which not only governs how things look when they fall but how they look when they move in general) is also proportionally less, giving it the ‘slow-motion’ look. I’m sure many will post much more indepth answers, but that’s the jist of it.
It’s the equations, man. The equations!
Basically, the acceleration from gravity is smaller on the moon than it is on Earth. About 1/6 as big, as you said. What this means for your spaceman leaping happily on the moon is that if he jumps with the same force from his legs, he gets pulled down to the surface of the moon only 1/6 as much. So he goes further and comes back slower and the whole process takes longer.
Now for the equations. Let’s say that you can throw a ball into the air so that it stays up for 5 seconds. This works out to throwing the ball 100 feet up at about 55 mph. On Earth. That’s because the height of an object after t seconds on Earth is given by
h(t) = -16t^2 - 80t
where the 80 is the initial velocity (in feet per second) and -16 is one half the acceleration of gravity on Earth (32 feet per second per second).
Now what about on the Moon? On the moon the gravitational acceleration is slightly less than 1/6 that on Earth. Let’s call it 6 ft/s^2 (feet per second per second) because it will make the numbers work out nicer. 
If we put out values back into our equation, we get that the height of the ball thrown on the Moon after t seconds is
H(t) = -3t^2 + 80t.
The -3 is one half the acceleration of gravity on the Moon, and the 80 stays the same, because it’s how fast we’re throwing that baseball.
Now, the ball lands when the height is 0 feet above the ground. When is this? Well, we need to wait until t=80/3 seconds, or about 20.3 seconds. How high does the ball go? It gets to it’s highest point halfway between going up and coming down. That is, when t=40/3. The height at that point is 400 feet. Yikes!
The 200lb man jumping into the air still has the upwards momentum of a 200lb man, but there’s only 33lb of force pulling him back down. It’ll get him in the end, but it takes longer.
Thought experiment: On Earth, put him in a big-ass helium balloon, enough to lift 167lb of his weight. He plus the balloon still masses 200lb, but now when he jumps there’s the buoyancy of the balloon slowing his descent. He’ll bob around just like your moonwalker.
Similar: Take a grandfather clock to the Moon and start the pendulum. Momentum keeps it swinging one way, gravity reverses it. So it takes longer for gravity to overcome momentum on each swing, and the pendulum runs very slow.
To condense what everyone has said:
Weight depends on (1) mass and (2) gravitational acceleration.
The earth kid ways less than the earth man because his mass is less.
The moon man ways less than the earth man because the gravitational acceleration is less.
You need lower gravitational acceleration to do the slow motion jump thing.