The most common favorite is not the definition of democracy - it's just the method of choosing that is most common. It's sort of self-justifying; "it's what we've always done, so we should keep doing it". But, things change over time, and we have the ability to better understand large groups of preferences than we used to (when counting first choices was the only possible way to vote), which means a better ability to provide social utility and help a group of voters help themselves in the most useful way.
Anyway, ordinal method doesn't actually apply any "weight" to a 4+ choice. The concept of "weight" doesn't actually apply to a Condorcet method. All you're really communicating is that you prefer candidate #4 to candidate #5, and to candidate #6, etc. There's no extra proportional "power" or weight given to higher-ranked candidates, though, because you've already communicated that you prefer candidate #1 to all of them.
It really is the same thing as if someone gave you (n(n-1))/2 ballots of one candidate against one other, with you picking your favorite. It's just faster to communicate in ranked form. It also doesn't run afoul of "one-person, one-vote", because no voter has extra power compared to another voter.
Finally, yes - say that 49% prefer A, have B as a close second, and hate C. 49% prefer C, have B as a close second, and hate A. 2% prefer B and hate both A and C. B's definitely just the "least objectionable", but also should definitely win as the consensus choice, even though B only got 2% first-place votes.