No - there is no size recommendation for SEO purposes. But it is recommended that you try and keep the image resolution low with respect to memory size (not physical size) - that is to say high quality vs low quality. You don't need high resolution for computer monitors.
The other reason is for image load time with respect to how long it take to download your website page to the visitor browser. However, with today's high speed computers and browsers, the image size is also becoming not so important. I personally don't worry about the size of my images anymore. BUT it could make a difference if you had a lot of images on the same page or post.