Washington was first president to use EA, while there has been greater willingness to use them in last fifty years (about 95% of all US international agreements, of which there have been more than 10,000), presidents between 1839-1889 signed more agreements than treaties (238- 215) and those between 1889-1929 signed twice as many of former (763-382).
As for framers of constitution, they were of several minds on treaty matter during the course of 1787 convention. Until very late, they had Senate, not president, making treaties. By end, however, they shifted power to president, giving Senate secondary role by requiring 2/3rds vote of consent. Along way, delegates defeated proposal by Madison that would have given Senate its own treaty-making powers independent of president.
EA's corrsespond to Marx & Engels' _Communist Manifesto_ characterization of the 'executive of the modern state...managing the common affairs of the whole bourgeoisie' and they exemplify circumstance that Marx called 'parliamentary cretinism' in _18th Brumaire_ - self-deception of powerless assemblies vis-a-vis executive.
Prior to 1972, presidents would make secret executive agreements. Congress passed legislation (over Nixon veto, if memory serves) requiring executive to report all EA's to Congress within sixty days. Neither Nixon nor Ford fully complied by reporting all agreements so, in 1977, Congress passed legislation (signed by new occupant of temporarily weakened office, Carter) requiring that Congress be informed of any oral/written agreement that might constitute inter- national commitment by US. Michael Hoover