It isn't so much that he did something but rather failed to do something. When it comes down to it, Louis XVI was treated poorly simply because he was the reigning king of France. At worst, he continued to live the life of the King that Louis XIV had started, which demanded massive wealth and massive expenditure but in reality he had to continue the payment of debts accumulated by Louis XIV and XV, the former famously pushed France to war several times and did expand her borders but also financed war through loans; Louis XV did the same but failed to succeed in any of France's goals. Combined with the debts of a century and a half of war and extreme luxury, France was going to fail in respect to economics.

Then when the Revolution starts, the French people look at the luxurious life style compared to their own lives and blame Louis for not doing much to fix France's current economic position (there is a lot more here, there is a difference between culture and economics but I can't understate how much Louis was forced to the life of King that he detested simply because he was expected to live the life of Louis XIV).

However, once the Revolution was underway, he wanted to assert authority during the Revolution and tried to prevent Revolutionary ideology from becoming de facto law; he was basically forced to sign the French Constitution and vetoed many laws that were aimed at establishing revolutionary ideals of equality. Combine that with the attempted flight of the Royal Family, Louis had shown himself to be apathetic to the Revolution itself (but he himself felt terrible about the position of the people).

In history, we say that the victory writes the history but sometimes the inability of some people forces history to be made. Louis was a good man that was born into a position that demanded a personality that wasn't his and events led to poor reactions against that position. While I can't say that he's a tyrant, I won't say that he tried to help the Revolution and sometimes worked against it.