What is the constitutional reasoning behind the decision in Citizens United?

Simply put, Citizens United v. Federal Election Commission is a First Amendment case. The First Amendment rights at issue are freedom of speech and freedom of the press. The Bipartisan Campaign Reform Act (BRCA), passed in 2002, prevented an "electioneering communication," advertising or a broadcast about political candidates sixty days before a general election or thirty days before a primary, and prohibited organizations such as corporations and unions from using their money for such broadcasts.  The court upheld the sections of BRCA that required disclosure of sponsorship but did strike down the other aspects, the prohibition against such expenditures and the timing constraints.  Michael Moore's movie, Fahrenheit 9/11 had been the subject of a complaint to the Federal Election Commission by Citizens United, a non-profit conservative group, but investigation concluded that his film was commercial activity.  Moore is in the business of making movies. Citizens United decided they were now in the film business, too, and the film at issue in the case was one that was designed to discourage people from voting for Hillary Clinton, entitled Hillary, the Movie, which sounds fairly neutral on its face.  The District Court below held that BRCA precluded advertising the film or showing it at all within the time constraints of the statute.  
The Supreme Court ruled that since corporations and other associations had freedom of speech and freedom of the press under the First Amendment, those portions of BRCA that interfered with these rights  were unconstitutional, and they were struck down.  To stop corporations and unions from spending money to present their political points of view results in the repression of speech, as does this blanket constraint of time, place, and manner, according to the court.  Similarly, the court argued, since the freedom of the press is for associations, not just for individuals, and since broadcast media are part of "the press," the BRCA could not pass constitutional muster, either.  There is no question that political speech is the most "sacred" in the First Amendment cases, and the idea was that any statute that allowed government to limit, repress, or suppress political speech should be struck down.
All of this sounds quite logical and reasonable, the Supreme Court protecting us from big, bad government, but this case and many others have created a landscape in which corporations are afforded far more political power than everyday people by virtue of their coffers, and this is a grave concern in a country that purports to be "of the people."