The simplest answer is: no, an object's weight usually will not change its falling speed. For example, you can test this by dropping a bowling ball and a basketball from the same height at the same time--they should fall at the same speed and land at the same time.

But that's not always true if there is a lot of drag such as air resistance. Air resistance happens because objects bump into lots of air molecules as they fall. The air molecules get knocked away and take some of the kinetic energy away from the object, which makes the object slow down. For example, if you drop a styrofoam cup and a metal cup the same way, the metal cup might reach the ground first. This is because the weight of the metal cup gives it more inertia, which makes forces like drag affect it less.

Sometimes, people will use their knowledge of air resistance to make things move faster or slower. Parachutes are designed to have a lot of air resistance and fall as slow as possible. On the other hand, the noses of planes are designed to "cut through the air," which is a way of saying they have low air resistance.

In physics, no - all objects fall at exactly the same rate. However, air slows down falling objects, so on Earth (or any planet with an atmosphere) a heavier object will reach the ground in less time. To see what happens to falling objects without air, watch this video:

In real life, heavier objects sometimes fall faster than light objects, but not because of gravity. Gravity makes all objects increase their speed at the same rate, regardless of how big they are. But if you drop 2 things outside, the air molecules may slow down one thing more than another.

For instance, a rock will be slowed down less by the air molecules than a feather because of their different shapes. But if you drop a rock and a feather in a vacuum, which is somewhere without any air, then they will fall at the same exact speed. The experiment of dropping things in a vacuum has actually been done and it has shown that they objects do fall at the same rate.

Some times. In the absence of air resistance, all objects will accelerate towards the source of gravity with the same rate. This was nicely demonstrated on the moon when an astronaut dropped a feather and a hammer, and they both took the same time to fall towards the surface of the moon.

On Earth, there is much more atmosphere than on the moon (which is very convenient for sustaining life, I might add), so air resistance becomes important in some cases. For objects with very low density or with very high surface area (such as a feather, or a kite), the air might exert a strong enough force to slow the descent of an object, or even lift it up if the wind is blowing strongly enough. (Things like dust can stay floating for a long time if the particles are small enough.)

So, if you're on Earth where objects are falling through air, a heavier object may fall faster than a similarly-sized lighter object, but it usually won't be noticeable to us because the effect is often quite small for most things we deal with in practice. (That is to say, bigger than a tennis ball, and falling from a height of ~1-10 feet)