Yes that is a screenshot of my registry for the key that I mentioned ("HKCU\SOFTWARE\Microsoft\Windows\CurrentVersion\Run" see image.) and there are no duplicates in my msconfig, Startup tab either.
So I don't know why one would be setup, I wonder if it might somehow be related to trying to install avast on a limited user account.
In any case, if you run msconfig you can uncheck the duplicate (not delete it) for the "HKCU\SOFTWARE\Microsoft\Windows\CurrentVersion\Run" entry for avastUI.exe, apply the change, click OK to exit msconfig and reboot.
That should mean that only one occurrence of the avastUI.exe will be run.