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The "Edit Current Profile" in "Settings" is buggy in the current konsole ( Version 16.04.1 on 2016-05-26 .) In particular, changes to font size are not saved.
I found it possible to edit the ~/.local/share/konsole/Profile\ 1.profile directly with a text editor:
# Following two lines added by troydwill to change font size to 16
[Appearance]
Font=Oxygen Mono,16,-1,7,50,0,0,0,0,0
[General]
Name=Profile #1
Parent=FALLBACK/
For folks interested relevant upstream bug report "Modifying the default profile does not work" is at https://bugs.kde.org/show_bug.cgi?id=358083.
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