It seems almost entirely irrelevant. So a company could have a reverse 2 for 1 split, and double its weighting in the average? How can one of the most popular barometers of the stock market be computed this way? What's the justification for weighting by share price rather than by market cap?
The share-price weighting of the DJIA is a historical artifact. The DJIA remains share-price weighted today because that's the way it has always been done, and we're talking about an index with more than a hundred years' history. The DJIA was first calculated on May 26, 1896. Perhaps, back then, price-weighting was the most straight-forward & feasible way to calculate it each day.
You're right that it doesn't make a lot of sense, and that's why the S&P500 and other indexes are better barometers.