The idea that dithering should be used to reduce your image size is a misunderstanding of image compression. Dithering is a technique which allows you to represent a color image with a very limited palette, in particular a two bit palette. The result is not much like a normal photo, but much better than nothing if you have a machine that can only output a few colors. (You could think of that as a sort of compression…
As I understand it, JPEG compression does not play nice with dithering as it is based on a matrix of discrete cosine transformations. Smooth transitions from one color to the next are much easier to compress this way than highly detailed features (i.e. a series of small dots due to dithering). For example, if you blur out parts of a photo, you will likely get a smaller image at the same compression level as the original. In other words, dithering basically creates a much harder image for the JPEG algorithm to compress.