I've downloaded and installed a deb package of Ubuntu Tweak from its website: http://ubuntu-tweak.com/. Is there a way to watch for updates for the package like packages which are in a repository?
No, manually installed packages can not be updated automatically.
However whenever a package we had installed manually will become available through our software sources we will get an update if the version in the repositories was higher.
To obtain similar comfortable updates for any application that did not make its way to the repositories we can watch out for a personal package archive (PPA) that may provide up-to-date versions of an application we need.
For ubuntu-tweak the "offcial" PPA repository with build for Ubuntu <= 14.04 can be added by:
sudo add-apt-repository ppa:tualatrix/ppa
or through the Software Center File > Edit > Software Sources....
We then also have to update our apt cache and can install the application with:
sudo apt-get update sudo apt-get install ubuntu-tweak