Clarification:

Here's a little argument as to why the charge density increases as the radius decreases:

Consider two conducting spheres connected by a wire.
Let us give the 'system' a charge Q. This charge will distribute itself between the two spheres.

Finally, let the charges on the two spheres be q1 and q2. Can you prove that:

q1/(4*pi*r1^2) is greater than q2/(4*pi*r2^2)? This implies that the charge density is higher on the smaller sphere.