The reason a bowling ball feels easier to pick up on the Moon than on Earth is because:
The weight of the bowling ball is less on the Moon than on Earth.
Weight is the force exerted by gravity on an object, and since the Moon's gravitational pull is about 1/6th that of Earth's, the effective weight of the bowling ball is much lower on the Moon, making it easier to lift. The mass of the bowling ball remains the same regardless of location; it does not change whether it is on Earth or the Moon.