Instead of creating jpgs using the "Save as" function, for files you are planning to upload, use the "save for web" feature. It makes much smaller files to begin with (no EXIF data, for one thing) and you can adjust the pixel dimensions there quite easily. Remember that a small monitor screen is only about 600 pixels or so across. If your photo is wider than that, some people will have to scroll to see it all. Just be sure that "constrain proportions" is checked.
Using save for web you can make a very small file for web use. HTH