My guess is that the files are saved as .jpg right? Jpegs are compressed. Your printer (software) is probably converting the image to a bitmap or some other uncompressed format. A 8.5" x 11" document @ 300ppi (pixels per inch, screen resolution - not to be confused with DPI, a measurement of printer resolution) is ~24MB.
Also note that (in general) the file size has very little to do with how much (total) ink is used. Ink usage is determined by the settings in the printer driver [Printer resolution; economy; 300dpi; 360dpi; 600dpi; 720dpi; 720x1440dpi] - [Paper setting; Photo paper; glossy paper; matte paper; other paper]
Think of screen resolution (ppi, sometimes called dpi) - as a measure of detail a file has.
Think of print resolution (dpi) - as a measure of how much ink is used by the printer. (The higher the resolution, the closer the dots of ink, the more ink is used.)
You can print a low (screen) resolution (ppi) image at a high dpi (which uses more ink), but will not increase the detail of the image.
Hope this clears up more confusion than it creates.