> What's special about the state or state government specifically that it should get its representation separate from the people it governs?
The United States is a union of states. The people have representation at the federal level, and the state level.
> Are the state or state government's aims and objectives different from the people of the state? If so, why, and what legitimacy does it have? If not, why have it represented?
No. The people of the state are the state, not the government of the state. Again, the state gets representation because we are a union of states. And local governments get representation at the state level. There are many concerns of a people, and we have people representing those concerns at different levels of government, from local to state to federal. Otherwise we could just have a single person represent everyone.
> Why does the state get represented twice (Senate and EC) but the people only get represented once? Isn't that an imbalance?
The People are represented twice as said before (House and EC). The EC is the House + Senate. So no, it's not an imbalance.
> Because it favors your side. You'd be singing a different tune if it was the other way around.
I don't have a side. I vote for policies that I agree with, which has changed over time. Party support of certain issues has changed over time as well.
I am pretty tired, however, of people crying about foundational aspects of my country because they lost an election. I think the increasing concentration of power in the federal government is a bad idea.