"…of giving to the State governments such an agency in the formation of the federal government as must secure the authority of the former, and may form a convenient link between the two systems."
The purpose of the US Senate was not in order to represent the population of the states but rather to give to the State governments an agency within the national government, so that there might be a link of compatibility between the national system and the state system.
This posting takes quotations from those living at the time the Constitution was drafted as to why the Congress was set up in this fashion.
As to why there are two houses (even though under the previous arrangement there was only one) and the reason why there make-up is determined by different criteria:
"If indeed it be right, that among a people thoroughly incorporated into one nation, every district ought to have a PROPORTIONAL share in the government, and that among independent and sovereign States, bound together by a simple league, the parties, however unequal in size, ought to have an EQUAL share in the common councils, it does not appear to be without some reason that in a compound republic, partaking both of the national and federal character, the government ought to be founded on a mixture of the principles of proportional and equal representation."
Those who spread misinformation do not want the states to be "independent and sovereign States, bound together by a simple league" but that is what the framers of the Constitution had in mind when they wrote the Constitution in spite of the misinformation which is taught in many schools today.
The small states such as Delaware, Rhode Island, and New Hampshire were afraid that the big slave holding states like Virginia would dominate and so the Senate was designed to protect these small states from being swallowed up by the large states into a monolithic republic:
"the equal vote allowed to each State is at once a constitutional recognition of the portion of sovereignty remaining in the individual States, and an instrument for preserving that residuary sovereignty. So far the equality ought to be no less acceptable to the large than to the
small States; since they are not less solicitous to guard, by every possible expedient, against an improper consolidation of the States into one simple republic."
I have heard it suggested on NPR that the purpose of the Electoral College was to protect the rights of the slave-holding states when in actuality the exact opposite was true. If the presidency had been decided by simple majority, the slave holding states would have far surpassed the votes of the states which had abolitionist viewpoints.
One of the main reasons for setting up this system was to prevent the large slave holding states from dominating over the small states.
"No law or resolution can now be passed without the concurrence, first, of a majority of the people, and then, of a majority of the States. It must be acknowledged that this complicated check on legislation may in some instances be injurious as well as beneficial; and that the peculiar defense which it involves in favor of the smaller States, would be more rational, if any interests common to them, and distinct from those of the other States, would otherwise be exposed to peculiar danger. But as the larger States will always be able, by their power over the supplies, to defeat unreasonable exertions of this prerogative of the lesser States, and as the faculty and excess of law-making seem to be the diseases to which our governments are most liable, it is not impossible that this part of the Constitution may be more convenient in practice than it appears to many in contemplation."
Another reason that was given for why the two houses of Congress would be selected differently and why there composition would be determined by differing criteria is so that both houses would prevent the other house from engaging in a betrayal of the public for the selfish benefit of the elected.
"It doubles the security to the people, by requiring the concurrence of two distinct bodies in schemes of usurpation or perfidy, where the ambition or corruption of one would otherwise be sufficient."
"it must be politic to distinguish them from each other by every circumstance which will consist with a due harmony in all proper measures, and with the genuine principles of republican government."
There is a movement to make the two houses of Congress so much alike that there is little or no reason for two separate bodies to exist. If the Senate is no different from the House then it is redundant and valueless.