Your comments

It doesn't work in browsers that use one of the supported browsers as its backend (one example of such browser is K-Meleon).

Someone must be including malware with Unchecky since it does nothing of the sort when its running.
Unchecky doesn't do anything of the sorts when it is being installed. You must've gotten an offer that wasn't unchecked by it when installing a program.
Why would you need to register it since its freeware? Also, no one can uninstall software as easily as you want. They need to connect to your computer remotely by way of TeamViewer, etc. You must've gotten a bad version of it from somewhere.
Maybe he/she got Unchecky from a site that is bundling adware/etc. with it?
Please provide a direct link to the installer that contains those offers. Thanks in advance.
Please provide a direct link to the installer that contains those offers. Thanks in advance.
Please provide a direct link to the installer that contains those offers. Thanks in advance.
Please provide a direct link to the installer that contains those offers. Thanks in advance.
Please provide a direct link to the installer that contains those offers. Thanks in advance.