They both mean that he has spent the evenings watching TV this week. The first (has been watching) puts more emphasis on the time it must have taken and is slightly more pejorative in tone. The second (has watched) puts emphasis on the fact, and, obviously, is slightly less critical in tone; indeed it could be an emotively neutral statement of fact.
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TuongvanHe has watched TV every night this weekWhere the focus is on the week: The speaker views the period of TV watching as closed, complete. The speaker is only interested in events that hav