This news is a little underwhelming, to be honest. First of all, it's a major exaggeration to say the weights have "never" been changed. They've been tweaked and altered a lot as newer technology with more precision in measurement was created. But that's just a minor issue with the hyping. As for the meat of the news.. well, the weights listed on the Periodic Table aren't really specific weights of that element. They're weighted averages based on the prevalence of different isotopes of that element in the natural world.
It's cool that they found that a single isotope's weight can change slightly, but it's far less mindblowing of a discovery than the article would like you to believe.