The reason uTorrent can stay small is because it exploits libraries that have existed in Windows since NT, mostly for GUI work. There was also development that incorporated the HTML Application library [1]. At least that was the case when I worked on it back in 2014.
I am specifically referencing the original PC version. There's a whole other library in the code dedicated to the mac platform implementation, as well as Linux. The reason uTorrent on Windows started small was because it didn't include much of any static linkages, but this depended on dynamically linking some libraries in Windows that Microsoft never removed. This is the dedication to backwards-compatibility I refer to.