How to specify font size in url other than \small \tiny?

Use the dpi setting, which effectively allows you to have any size you want, i.e.

http://latex.codecogs.com/latex.gif?80dpi sin(x^2)
http://latex.codecogs.com/latex.gif?280dpi sin(x^2)

Which gives: and

I should add a small health warning. Some latex fonts (or graphics) are designed by combining several character. For example a long arrow may be made from a straight line and a normal arrow. Using different fonts and dpi can lead to miss-alignments or different thickness for different parts. If you find any problems please report them back here - they might be fixable.