Sports are like opera or Shakespeare for the working class. You'll pretty much see the typical "macho" man cry at two places; a funeral, and a sporting event. People might think it's barbaric to be into sports, but in many ways you are watching something very human and emotionally charged unfold in front of your eyes. Most of the people involved on the field/court/rink have very strong vested interests in what is happen, and strong emotional connections with their teamates.
Given that many people live lives where there's very little outlet for creativity and culture, sports can be a way to live vicariously, or at least share the feeling of the struggle and the human experience with someone on some field. Granted, the life of a pro athlete is undoubtedly better than 99% of the people who make up their fan base, but everyone on the planet faces triumphs and crushing losses, and sports is a very quantifiable, simple way to experience this. As for it being plebian, I'll evaluate that on a case by case basis. I know a number of highly cultured and highly intelligent people who are very into sports, and I don't think less of them. I'm into sports and act like a total idiot when I watch it, so if some associate lawyer with a monicle listening to his Naxos recording of the Four Seasons wants to call me a pleb for liking sports, then I don't want to be "sophisticated and cultured".