If you have embedded images, that is most likely the problem. In SVGs, embedded raster images are still raster images, not vectors. The size of the raster image will be the limiting factor here.

You probably need to open the raster image in a raster editor such as Photoshop, then export as JPEG so you can add a bit more compression to get the file size smaller, or even resample the image to make it smaller (lower resolution), or a combination of both. Then embed the image in Illustrator, and export as SVG.

If you choose to preserve Illustrator editing abilities, that will make the file size even bigger as it will also embed the whole illustrator document inside the SVG.

If you choose to link images files instead of embedding them, then you will have to also upload the linked images files somewhere if anybody else opening the file is to see them. So, that probably isn't practical.

One more thing to note, SVG might not be the best format for what you are trying to do.  Might be better to export as PDF, since it is designed specifically for print. Also with Illustrator, you can choose the amount of compression to add and also include resampling to reduce image sizes when exporting PDFs from within the PDF export dialog.