Most videos on YouTube are loud enough and I can hear them perfectly well, but some have got the volume down too low even with the YouTube volume slider on max and the PC volume set to maximum too. In theory it must be possible to increase the volume, but does such software actually exist?
There is a browser add-on for Google Chrome and Firefox available and actively maintained as of 2019:
Apparently it's not just for YouTube, but that's what I needed something for a few years ago, and that's what I needed again now. This time I found it and it's working for me right now.
It has a pre-amplifier and also a graphic equalizer. I'm only using the amp.
Presumably flash is accessing you audio at the driver level so the only change you could make would be there i.e. using a driver that lets you route the audio through processing (It might be worth looking into this http://jackaudio.org/ I'm not sure this will do do the job).
I use this bookmarklet:
Apparently, YouTube videos are normalized, so the video volume is not 1.0, it ranges from 0.4 to 0.7 on some videos.
I explained this here