They believed in a very, very tiny government because they had a very, very tiny economy
Another simplistic, liberal,
i.e., progressive, assumption. Americans were quite well off and happy. They were one of the most properous people of the eighteenth century, having been perhaps the key players in turning England's strugggling, limited trade relations with northern Europe into a sophisticated trans-oceanic commercial network that transformed the tiny, insular country of 1600 into the world's dominant power by 1700.
The Americans were perhaps also the most liberated people of the eighteenth century. The Crown retained some authority in the colonial courts and legislatures, in America's international relations, in the expanses of wilderness to the west and a few settled territories in the east. It established the colonial post office, regulated naturalization, and retained a few other powers here and there, such as the power to collect fees, dues, and rents, but the great majority of the organs of government were held by the colonists. American agencies maintained law and order, administered justice, and in general regulated everyday life (personal conduct, the worship of God, taxation, the production and distribution of wealth, etc.). The Americans condemned the prerogative power of the crown.
The Americans were already allying with other European powers. They were by no means insignificant.
They believed in a "very, very tiny government" not because they had a "very, very tiny economy," which is a laughable assumption, but becasue they wanted to preserve their society and way of life.