does this mean that correct writing carries more weight?

Actually, correct writing carries less weight, B-Y, because there is less of it when it's done correctly. That's speaking volumetrically*, of course.

Have you noticed? The best writers can speak volumes without writing volumes. Publishers love that. It saves them a lot of grammage. [I wonder if there is a connection between "grammage" and "dunnage". Newspapers took their masthead from sailing ships so maybe they took their dunnage from that source as well. No-one wants to add ballast to a newspaper. It's just dead weight.]

* But qualitatively? Who could disagree with you? :)