ok, i was a little harsh about the bird rights, theres pros and cons to it, but if you think bird rights or even the nba salary cap rules for that matter create a level playing field for big and small market teams, your mistaken imo. The cavs just paid 54m in luxury taxes (the salary cap was 84.7m) to win a championship. You really think every team in the league could afford that? Now granted thats a record number, but even the 2 next best teams (warriors and thunder) spent over 14m in luxury taxes. The NBA's salary cap has been far from perfect and theres a reason its always changing and getting stricter. Id even argue that the stricter cap rules have made the NBA more competitive and in turn way more popular which is why youve seen the huge cap increases these past 2 years (and more to come).
as to you're original question, the past few nba champions have been:
2016 Cleveland Cavaliers
2015 Golden State Warriors
2014 San Antonio Spurs
2013 Miami Heat
2012 Miami Heat
2011 Dallas Mavericks
2010 Los Angeles Lakers
2009 Los Angeles Lakers
2008 Boston Celtics
2007 San Antonio Spurs
2006 Miami Heat
2005 San Antonio Spurs
2004 Detroit Pistons
2003 San Antonio Spurs
2002 Los Angeles Lakers
2001 Los Angeles Lakers
2000 Los Angeles Lakers
In 16 years there has only been 8 different teams to win a championship, with 3 teams owning 12 of them, so clearly its really not that well balanced. As for the small market vs big markets, you can only make a case for 3 of those teams being small market (spurs, heat, cavs). The cavs spent a record high luxury tax for their sole win, 2 of the 3 heats titles came with the big 3 and high luxury taxes of their own, and the spurs have for years gotten cheap deals from their stars. once the pelicans, grizzlies, bucks, etc start competing for nba titles then you got a case big and small market teams have been winning titles