I don't disagree with weighted votes per se, but saying "6 downvotes" really is misleading, if there were actually less than 6 votes.
I wonder whether it would be helpful to display the karma in analog form, for example as a line, where longer line would mean more total votes (not in linear proportion, but in a way where infinite number of votes asymptotically corresponds to the full width of the used part of page), and the line has a green part and gray part whose length ratio represents the upvotes/downvotes ratio. And of course tooltip for number, but the idea is that people would get the right idea without seeing the numbers.
I agree that it's misleading. One thing that's been mooted -- I don't know whether it's in any way likely to happen, but it seems like it would be an improvement -- is changing from "a level-n user's vote is worth n points" to "a level-n user can vote up to n times on anything". Then if you wanted to use your awesome multi-voting power (1) you'd have to expend at least a little extra effort, (2) you would have the option of giving intermediate numbers of votes, and (3) it would no longer be wrong to say "this got 7 upvotes and 3 downvotes" or whatever.
The analogue-karma-display idea is intriguing. My immediate feeling is that it would be really hard to make this comprehensible, though.
What are your first impressions of the public beta?