The New York Times color schemes is, well, black. Its titles are black. Its bylines are black. Its body copy is black. Its rules are black. Everything is black. The only color used in The New York Times is its pictures and its ads.
The reasoning behind using weight, style, and size to separate its content rather than using color is to get across that the Times is a very serious and reputable publication. They want to sell papers based solely on their reputation and content and not worry much about design (clearly).
One positive result of their very stern stance against color is that it makes the photos (the only elements featured in color) pop. The colorful images, set against the pure white and black of the rest of the paper, makes the colors of the images look especially vibrant and striking. This could be another reason the Times chooses not to use color in their body.
One problematic consequence of using no color in the papers content is that the ads, which are in color and often take up the whole width of the page, dominate the content and stick out more than any reader would want them to.