The sun gets smaller and smaller as it moves away and the light gets dimmer and dimmer as well! Just see how far you can see on a dark night, traveling in the country, with your headlights.

Except the sun does not get smaller throughout the day. Have you actually looked at the sun before?
This is from the light source perspective, in this case a car. However, if you were on a hill ten miles away with direct line of sight, you would be able to see these headlights in the distance, even though they do not light up the area around you at all! And these lights will get larger and larger as they get closer, despite all the atmosphere in the way.