I offer some insight here, hopefully. When you embed the image and also create a pdf compatible ai file it embeds the file twice one for the ai file and the other for the pdf version of the file. The file size includes twice the image data so it will be considerable. If you turn off this option it will reduce the file size but you will not be able to place the file in another program with a preview as the preview is a part of the pdf data. Not only that but you will not be able to print the file to a non-postscript printer that is it must be outputted through the postscript process or if you wish a postscript driver. In the past the generally accepted and recommended method was to link the image as a way of working and maintaining a smaller size file and then use the Include Linked Images option in the Illustrator Save Options dialog so only the file you sent the printer would be large. Of course if you are like me and make back ups of everything then you would now have a copy of what you sent the printer as well and the original file which would take more space than a single file with the embedded image. The more modern way of doing this is to work with the link file and then save it as a pdf as well the pdf will be considerably smaller in size and the linked ai file will be as well together they will be about the same as an ai file with the pdf compatibility turn off which is another way of doing this which is fine if you are not placing or opening the file in another application or sending it to a non postscript driver for output. I recommend for your purposes to work linked, the traditional way, and output to pdf and send the pdf to the printer or if you are a member of the Cloud link the image and use the new collect for output mechanism which will collect you file images and fonts for out put in a neat folder for you, or at least that is what I understand. This is only a suggestion not a directive, it is meant to be helpful. Please feel free to ignore it entirely if it does not suit your needs.
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