Use "I've been ___" to describe a situation that's been continuing for some length of time, and is still happening:
I've been married for 15 years.
I've been waiting for you to get ready.
I know that I haven't been a very good friend to you over the past few years, but I hope that you can forgive me.
In the example at top, the speaker hasn't been watching the TV constantly for the past week, of course. But he's continued to watch it again and again. And since the speaker said "I've been glued..." instead of "I was glued...", that means that he's probably going to continue to watch it.