Federalist #62, section III:
"The equality of representation in the Senate is another point, which, being evidently the result of compromise between the opposite pretensions of the large and the small States, does not call for much discussion. 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. But it is superfluous to try, by the standard of theory, a part of the Constitution which is allowed on all hands to be the result, not of theory, but "of a spirit of amity, and that mutual deference and concession which the peculiarity of our political situation rendered indispensable.'' A common government, with powers equal to its objects, is called for by the voice, and still more loudly by the political situation, of America. A government founded on principles more consonant to the wishes of the larger States, is not likely to be obtained from the smaller States. The only option, then, for the former, lies between the proposed government and a government still more objectionable. Under this alternative, the advice of prudence must be to embrace the lesser evil; and, instead of indulging a fruitless anticipation of the possible mischiefs which may ensue, to contemplate rather the advantageous consequences which may qualify the sacrifice.
In this spirit it may be remarked, that 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.
Another advantage accruing from this ingredient in the constitution of the Senate is, the additional impediment it must prove against improper acts of legislation. 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."
https://avalon.law.yale.edu/18th_century/fed62.asp