This suggestion for dealing with the small fonts in Outlook 2013 and 2016's folder list comes from Cowboy over at OutlookForums.
As we all know, Microsoft removed the ability to change the font and font size in the Outlook 2013 folder list. But all is not lost. For those people with high resolution monitors and/or poor vision there is something we can do short of enlarging the whole display image.
To change the font size in Windows 8/8.1, right-click on the desktop and choose Personalize then click Display. Click on the dropdown under Change only text size. You will see the items that you can change the text size are Title Bars, Menus, Message Boxes, Palette Titles, Icons and Tool Tips.
If you are using Windows 10, you'll need to open the Control Panel and find Display. Then change the Menu size.
Select Menus and choose a new font size.
You cannot change the font that is used, but you can change the size and make it bold.
I found if I just change the menus size from 9 to 10 it makes the folder list text larger. It also increases the size of the ribbon which in my case is fine. One client changed almost everything to 12 which I think is a little over the top, but he really likes it. So if you are having trouble reading text in Office 2013 applications, play around with it and I think you will be able make some adjustments which will really improve the look and feel of outlook and other applications as well.
Change Font size in Windows 8 Video Tutorial
In Windows 7, the Font settings are in Personalization > Windows Color. The Menu font and font size used by all applications can be changed. Because it is used by all applications, I don't recommend changing it more than a size or two.
Outlook 2010's folder list has it's own folder list font setting in View > Navigation Pane > Options.
More Screenshots are at Changing Folder and Message List Fonts.