How is political power distributed in America? why did the anti-federalists fear the new system and does the new system strengthen or weaken...

If we are examining the American political dynamic at the start of the Constitutional Convention, we can see that anti- federalists had much to fear.  Emerging from the shadow of King George and the British rule which caused the American Revolution, the anti- Federalists were  convinced of the need to hold individual rights and personal liberties as the critical shield against central government encroachment.  Even if the lack of a political order would make the nation susceptible to uprisings such as Shays' Rebellion, where farmers challenged the authority of the Massachusetts government and a central army was not sanctioned and therefor could not quell the disturbance, anti- Federalists believed that individual rights could not be overruled by any central authority.

On the other side of the coin, the Federalists were convinced of the need of a constiutitionally bound federal government as being essential to perform the functions and execute the well being of the state.  To not have one would bring the new nation close to anarchy.  Freedoms would not be worth having if domestic tranquility could not be preserved.  Both sides were afraid of the logical extreme of the other.

The issue of separation of powers was a portion of the solution to both sides' fears.  The idea of dividing government into three branches helped to ease the anti- federalist fear of strengthened central government as one government divided into branches posed less of a tyrannical threat than one unified entity.  At the same time, federalists believed that dividing power amongst the three branches would actually increase the efficiency of the government, as different aspects could be effectively addressed.  Madison's notion of checks and balances helped to fortify the beliefs that both sides could be happy with this arrangement as he believed that if one flower could not bloom, let a thousand of them flourish.  In this idea, one branch needed the other two in order to work to the best of their capacity.  This triangulation of power helped to provide the glue which served to keep the nation's political structure intact.