Self upvoting isn't the problem. The problem is when people self-upvote and no one else agrees the content is worthwhile. Quadratic weighting stops that, assuming everyone is equal in vote power. Because a post/comment with one vote will only get one ten thousandth of the reward (that is to say, nothing at all) compared to a post/comment with 100 votes.

In practice, people are not equal so this model is false, and it was largely false in the original whitepaper as well. What it really did was let orcas and whales self-upvote or vote for their friends or business partners while the bulk of the user base might as well not vote at all.