Persistent, Niggling Questions

[Tate]

It all boils down to the way things were when the Constitution was written. At that point, the States considered themselves to be sovereign entities, entitled to make their own decisions. The Constitution was framed so that the States and their populations would be fairly represented in the federal government. The legislature, for example, was divided into two bodies, with the Senate representing the States and the House of Representatives representing the population.

Likewise, the electoral collage was devised with the same number of electors per State as the total number of the State's Senators and Representatives, so that the States are each fairly represented in electing the President. So, yes, the smaller States get a bigger voice in the electoral process than they otherwise would have, because the framers of the Constitution were concerned about fairly representing the States, not just the people.
As time has gone on (especially after the American Civil War), the States have become less autonomous and the federal government has become more important, so the idea of representing States equally has become less relevant, but the Constitution's rules for presidential elections stay the same.

As for why some States give all their electors to one party while others split the electors, that goes back to the days of the Constitution too. The States were each given the right to choose their electors however they wanted. Originally, I believe, the State legislatures chose the electors directly, without consulting their populations at all. As time went on, democracy became more popular and the States started to choose their electors by popular election. Some let the majority party take all the electors, while others split the electors, just because they individually decided how to choose the electors.

I wish more States would split the electors according to the proportion of the popular vote each party received. My own State of California has 55 electors (over 10% of the electoral college) and these days they all go to the Democratic party. There's not much reason to vote either way, because there's a large enough Democratic majority to make it unlikely that the State would ever go to the Republican candidate. If the electors were split, there would be more of a contest and more reason to vote. But that's just my opinion.