How did thomas paine use concepts of equality, reason, and nature to criticize the legitimacy of monarchical government and british control of the colonies

Thomas Paine believed the selection of kings to be unnatural because people are born as kings and nothing assures that they'll be good leaders. He argues that nature disapproves otherwise there wouldn't be "an a** for a lion." He says that mankind is originally equal in order of creation. Says that the colonists have been wronged too many times to attempt reconciliation with the British. 

One common question taken up by Enlightenment philosophers was:  Does government have a responsibility to respect the rights of its citizens?

The Enlightenment philosophers tended to answer that question in the affirmative.  The idea of a "social contract" meant, in their view, that the government had obligations to the people who had empowered it.

Two examples would be John Locke and Jean-Jacques Rousseau.  Locke and Rousseau both argued that the people had the right to change a government that wasn't serving its intended purpose.  

Both Locke and Rousseau wrote political philosophy about how the people should be the sovereign power in a state -- that a government gets its power from the people and needs to serve the interests of the people.  So they supported the people's right to remove a government that has become tyrannical and replace it with a government that works properly on behalf of the people.  

American colonists took up arms against Britain in response to their sort of philosophy (especially Locke's).  And the bourgeoisie in France started the movement that became the French Revolution based on thoughts in both Lock and Rousseau.  But as Enlightenment thinkers, both men ideally hoped to convince others by means of their arguments that a constitutional form of government was the best idea (Locke), or even that direct democracy was the right way for a state to operate (Rousseau).   Their main concern was that government respect the rights of its citizens.