The short answer is, you may not be able to.
In fact, the problem is much worse than you think.
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Black isn’t black
The problem stems from the fact that, currently, outlook.com doesn’t display email in black text. It’s using a darker shade of gray.1 On a scale of 0 (black) to 255 (white), it’s approximately 31.
No, I can’t tell you why. It’s apparently a design trend to avoid using true black on white. Various sites and designs suffer from this problem.
Some allow you to change the color via a setting of some sort. Unfortunately, outlook.com’s “Theme” settings don’t affect the color of text.
And when you print an email, it prints the email as displayed. That means you’ll be printing grey text from Outlook.com. There’s no option not to.
Gray isn’t grey
Another problem you’re running into is that this particular shade of gray looks different on your printer than it does on your screen.
Depending on the brightness and contrast settings on your display device (which may or may not be available), that dark shade of gray on the screen probably never looked gray to you at all. It was close enough to black to be mistaken for it. It works both ways; I often hear from folks for whom even the darkest gray that isn’t exactly black looks obviously gray and washed out on their screen.
The same is true for printers. Gray is grayer on some printers than others. Occasionally it might be so dark as to be mistaken for black; on others, not so much.
Clearly, in your case it’s probably not noticeable on screen, but it is on paper.
Without settings, there’s little we can do, but there is at least one straw to grasp at: printing.
When printing your email message, examine the options in the Print dialog box.
If you have the option to print in black and white instead of color, choose that. Be sure to examine “More settings” and other settings that may be available for your specific printer if you can’t find it.
Naturally, there’s a catch: for some printers, printing in black and white really means printing in shades of gray, much like an old black-and-white television. The result, of course, is that we haven’t solved our problem at all. On the other hand, if black and white truly means only black and white for your printer, it might just work.
Print to PDF
A similar option is to select Microsoft Print to PDF as your printer — it includes a color selector that you can switch to black and white. NOTE: “Save as PDF” is a different option, and does not include the color choice.
This then saves a PDF to your hard disk. You can then open the created PDF in your installed PDF viewer (like Adobe Acrobat, or others) and print the PDF directly to your printer. It’s possible, though not entirely certain, that the result will be pure black and white
If it isn’t, I’m afraid I’ve run out of ideas.