I have a Surface Pro, and when travelling around I often hook up to a random second monitor. The default DPI scaling of the Surface monitor is 175%, while an external monitor in 1920x1200 resolution is set to 100%.
When running Skype for Business on the Surface monitor everything looks ok, but when I move a chat window over to the external screen, it all becomes super big.
I came across a post by Matt WoodWard which pointed me in the right direction but didn’t solve it for me.
I’m on Windows 10 Fall Creators Update (10.0.16299.19), and what did the trick for me was to open up the file C:\Program Files (x86)\Microsoft Office\root\Office16\LYNC.EXE.MANIFEST, and change dpiAwareness from PerMonitor to System. Remember to open the file as an administrator. If not you won’t be able to change it.
After quitting Skype for Business and restarting it, it all worked.