Are you saving it as a 72 ppi jpg? Also use your image editing software to "Save for Web" (Photoshop) or send as a low res email file or save as a jpg with lower quality. Any of these will strip unneeded data and reduce file size but still allow a decent sized pixel count.
It's easy. Downsize to 80 pixels or what-ever the site allows. You can cut an appropriate part out, and paste again to have the zoomed view.
When saving, you can adjust quality (data compression). You will succeed.