In a certain sense, America's founding fathers were terribly afraid of democracy, and went through great pains to mollify it with an extremely conservative system of government that deemphasized sheer population numbers. The people as a whole were feared for being fickle and unpredictable. The founding fathers did not want the federal government and country as a whole to change as a result of the current fads and emotional impulses. The House of Representatives, being directly elected by the people and in proportion to the number of people, would reflect that destabilizing fickleness.
The Senate, on the other hand, was initially designed to have its membership appointed by the State legislatures, not elected by the people. These were meant to be reasoned statesmen, who, combined with their much longer 6-year terms, could stand above the ephemeral fracas of the people and act in the greater and long-term interests of the states and the country as a whole. The fickle, fast-changing House was balanced by the slow and sartorial Senate. The same basic idea was used to rationalize the election of the President via Electors, rather than a direct, democratic vote by the people: the founders envisioned the electors as principled and intelligent men of strong moral fiber who could prevent the unfettered "will of the people" from electing a demagogue who gets by on vitriol and celebrity rather than an actual capacity to govern. Reality ultimately was much different, and electors these days are little more than puppets who are frequently penalized if they depart from the popular vote results, no matter the reason.
The States were also much more individualized, independent, and protective back then. None of them wanted to have the affairs of the entire country dictated by a small number of heavily populated states, whose affairs and priorities may be radically different.
As such the founders of the USA in fact endowed the Senate with substantially more power than the House had: they would confirm judges, cabinet members, etc. The only power the House has that the Senate does not is in the Origination Clause, requiring tax legislation to initiate in the House.