There are two kinds of messages.. direct, and broadcast.
The broadcast messages are those small "i" yahoo messages that consist of:
Yahoo! -- some ultra-short blurb -- SOURCE: REUTERS
The "news" is something really in-depth, like "Jason Priestly injured", or "Tensions rise in middle-east". Who writes this stuff?
As far as I know, there is no way to turn these off. They're broadcast to every pager on the network, and the watch has no way to "ignore" them. Fortunately, they don't beep or anything, so you can just ignore the "i" if you don't want your insipid piece of entertainment trivia for the hour. The watch remembers only the last one, so you never know if it will be sports, entertainment, world news, or market wrapup.
The direct messgages are aimed straight at your watch, and you do control those. You can select stock quotes or headlines to your liking, and they are actual pages. They're longer than the "info" junk, and beep the watch like any other page. You can select them at mobile.yahoo.com or wherever, since it's just email.