It is not all about image size - x pixels by y pixels. Jpeg is a compressed format so the size of the file is content-dependent. A photo with little detail can be compressed more than one with a lot of detail. When resizing for the 128K limit of this forum, it is important, in addition to specifying the number of pixels in each dimension, to specify the "JPEG quality" which is usually a number from 1 to 100. Higher quality results in greater detail which results in a larger file size.
The best thing is to use a program that allows you to specify the image size, as well as the maximum file size so that it can create a jpeg with the highest image quality.