Why small government? Why not big? In 1786, a central question on the framer’s minds was how to create a government strong enough to govern and defend all of the colonies without creating a new tyranny that would favor one political faction or one person’s ambition. The framers of our Constitution were generally in agreement that their original Articles of Confederation would not be sufficient to hold the colonies together. How could they create a government that all of the colonies could trust enough to support? That was the big worry as they went into the 1787 Constitutional Convention.
Their solution was to give the new federal government a just a short list of enumerated powers that it could exercise with strength. Those powers not specifically assigned to the federal government by the Constitution belong to the states or to the people. The federal government was made quite strong within its enumerated powers, notably for defense and foreign affairs. Thus, the question, small or large, isn’t pointed in the right direction. The framers intended a government small in its enumerated powers but large in its capacity.
There is more to the story. Why checks and balances? Why federalism? Why a Bill of Rights?
One more note: Many people mistakenly try to justify their arguments for or against policies related to taxation, spending, and regulation with references to the framer’s choice of limited enumerated powers and strong capacity. They are mixing apples and oranges. They are confusing arguments over policy choices with the rules by which policy arguments are settled.
 See for example Madison in Federalist 45 “The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite.”