I'm going to recommend a utility called
JPEGmini. It's available for both Mac and Windows, and unless you're doing nothing but processing JPEGs for a living, the
maximum you'll need to spend is $20. (The free "trial version", which is actually an unregistered full version, has a limit of 20 images/day, and that may be all you need.) Exporting your images at a relatively high quality (90-100 inLightroom or Gimp, 11 or 12 in Photoshop) and with minimum metadata (convert to sRGB, no embedded colour profile), then run through JPEGmini will result in images that are visually indistinguishable from your original high-quality output but about 1/6 to 1/5 of the file size, on average (like you had dropped down to a much lower quality export, but without any of the nasty artifacts). A 2K/"full HD" image (1920 x 1080) will ordinarily weigh in at between 150 and 300KB, depending on the level of detail, after being processed. Smaller images will, of course, be smaller.
No, I don't have any affiliation with JPEGmini. I'm just a really, really happy customer who saved a lot of hours and a lot of gigabytes of upload time/bandwidth without losing anything at all quality-wise. I've had it for a week, and it's already paid for itself a couple of times over in ISP overage charges.