There are a couple things you can try:

1) Edit the idlde.ini file
Windows: C:\Program Files\Harris\IDL88\bin\bin.x86_64\idlde.ini
Linux: /usr/local/harris/idl88/bin/bin.linux.x86_64/idlde/idlde.ini

Add this line under -vmargs:
-Dswt.autoScale=200

Possible settings for this parameter are detailed here: https://www.eclipse.org/eclipse/news/4.6/platform.php#swt-autoscale-tweaks

The default settings of "integer" doesn't appear aggressive enough or work at all. It is suggested the user experiment and set a value above 100 to their liking. With a value too large, everything becomes pixelated and too large.

2) Change this Windows 10 setting:

Windows 10: Use app scaling to make the entire app scale larger. This really just lowers the resolution of the app while maintaining high resolution for the operating system. The result is larger text and icons in IDLDE, but the whole workbench appears somewhat blurry. This also impacts all other apps on the PC.

Settings > Display > Scale & Layout > Change the Size of Text, Apps, and Other Items > Increase this % value

Thank you for the information about the -Dswt.autoScale=xxx setting in the idlde.ini file. This works to change the icon size. It appears this autoscale setting is applied instead of the Windows 10 scale setting. My Windows 10 scale is set at 150%, so the default integer setting and a value of 100 produced the same result (100% scale, i.e., the small icons that I saw in the first place). A setting of quarter and the value 150 gave the same icon sizes; a value of 200 also worked (double size), but a value of 175 resulted in no icons showing at all. The setting exact appears to make the icons take their scale directly from the Windows scale setting.
Thanks again.