I pay for The Economist not only for what it contains, but for what it lacks. There are no cat videos, no "top ten differences between men and women," no pop science fad of the day. I stopped reading the NYT because it has too much fluff, and their web design makes it difficult to find the substantive articles. Plus their "most emailed" list is just full of horrible clickbait which disappoints me every time. Really the NYT's sensationalist science/health fad reporting was enough to drive me elsewhere by itself; it made me stop trusting them as a reliable source. I know that The Economist is biased, but they are obviously biased in a particular way, not randomly careless. If I want the other side of the coin, I will read the New Yorker and the NYRB.
Also, I like the weekly format because it gives the journalists more time to write something thoughtful. As Chesterton put it:
"The tendency of all that is printed and much that is spoken to-day is to be, in the only true sense, behind the times. It is because it is always in a hurry that it is always too late. Give an ordinary man a day to write an article, and he will remember the things he has really heard latest; and may even, in the last glory of the sunset, begin to think of what he thinks himself. Give him an hour to write it, and he will think of the nearest text-book on the topic, and make the best mosaic he may out of classical quotations and old authorities. Give him ten minutes to write it and he will run screaming for refuge to the old nursery where he learnt his stalest proverbs, or the old school where he learnt his stalest politics. The quicker goes the journalist the slower go his thoughts. The result is the newspaper of our time, which every day can be delivered earlier and earlier, and which, every day, is less worth delivering at all."