I'm sorry, but you have this completely backwards.
Yes, I am aware of how the electoral college works, and what the House and Senate are. I have been voting since 1988. Specifically because the electoral college votes from a particular state include those granted by having two senators, low population states' popular vote carries more weight in electing a president (and vice president). I may have worded that badly before, I hope that was clearer.
The three-fifths compromise made it so that, for purposes of counting population, to decide how many representatives in the House a state had, every five slaves were to count as three persons. This gave the southern states a huge boost of power in the House - because slaves got counted to find out how many representatives they had, even though those slaves were in every other way property, with few rights, certainly not the right to vote in the elections for the reps their number served to create seats for.
Again, the fact that each state had two senators, and that those states were kept evenly split between slave and free states (or states which wanted to expand slavery and states which wanted to curtail or outlaw slavery) demonstrates how the balance of power in the senate was kept that way in order to avoid a conflict over the issue of slavery. Since states had different populations, and since much of the concentration of free people was concentrated in the northeast, the Senate (then as now) gives disproportionate power to (I mentioned this before) lower population and more rural states. Then, those states were largely southern slave states. Today, those states are largely rural conservative states.
Yes, of course, there were slaves in northern states, too, but far fewer, and many northern states were curtailing or outlawing slavery while the south was doing everything in its power not only to protect it in the south, but to expand it for all states.
Slavery was a divisive issue in the US from the very beginning, and the issue got kicked down the road many, many times before Lincoln was elected and the south seceded. Everything that happened at the federal level.