The stone itself is concave on the bottom so only a small amount of it is in contact with the ice. The ice is not smooth. Water is sprinkled on it so it has a pebbled, concrete-like texture kind of like Braille writing. Since the stone is traveling on this rough surface, the turning motion causes it to curl. The spin has to be slow or else the stone will not curl. The sweeping action creates friction that will actually melt a little of the ice and allow the stone to go straighter and farther.

The further out you throw {away from the center line} the less the stone will curl because it was pushed out to the side and has to "fight" that before it starts to spin in the direction you want. If you throw heavy weight on this website your accuracy will decrease with increased weight, it is because it was VERY easy to play big weight shots all game and got boring, so they added some flaw into big weight shots.

As the rock is rotating, one side of the running surface will always be moving faster than the other as it travels over the ice surface.
Example: When a rock traveling down the ice has a clockwise rotation, the left side of the rock is traveling faster over the ice than the right side.

There are several explanations of why rocks curl. Most of them are very technical and hard to follow. The following explanation is very straightforward and easy to understand. Some people may disagree with the exact details of why rocks curl.

The running edge of the rock that is moving faster is known as the "outside edge" and the slower side as the "inside edge". Objects moving faster create more friction. The faster edge has more friction than the slower edge. Because the fast side (the outside edge) has more friction, it causes more "frictional melting" of the ice. Since ice with a small layer of water on it is more slippery than dry ice, the slippery side (fast side or outside edge) bites the ice less. The slow side bites more causing it to "pivot" to the right. Therefore, a rock with a clockwise rotation will curl from left to right.
How Sweeping Works

The sweeping motion briefly polishes the ice just before the rock travels over it. Warming the ice slightly increases the overall frictional melting and allows the rock to continue moving. This results in the rock traveling farther. This is technically defined as decreasing the rate of deceleration. The overall reduction in friction has another effect: Since the rock is biting less on both sides, the rock will travel straighter.

Sweeping cannot make a rock move faster, only farther.

A couple of brilliant posts Mark; well done. You'll be writing a book next!

Give me $50,000 and I'll start writing.