"Lightweight" is one of those overloaded terms that can mean a lot of different things.
In Spring’s case—and please keep in mind that I am not a Spring expert—“lightweight” seems to mean a departure from the configuration/boilerplate-heavy style of previous Java web development frameworks.
Frameworks like Struts 1 involved writing lots of XML configuration files, classes full of “do nothing” code, and a complex directory structure for packaging applications. Spring, on the other hand, does its best to save you from having to repeat yourself in your code, and relies on naming conventions to reduce the number of configuration files needed to hook things together.
In theory, this reduction in code complexity will also come with improved performance, because applications are “lighter”—thus the term “lightweight.”
Someone, please, correct me if I’m wrong.