Weinberg doesn't answer my first question, since he makes no comment on anybody's, including his, current interest in explaining the equality and opposite polarity of the electron (a fundamental particle) and proton (a composite, not fundamental, particle). To me, the equal and opposite charge on these two very different particles is the most interesting mystery in physics. It's the reason we have atoms, and that's something that needs explaining in a theory!
In regard to Weinberg's use of the terms "symmetry group" and "electromagnetic gauge transformations" here are some quotes from Wikipedia: In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Even more difficultly obscure is "gauge transformation," which I'll get back to later.
For now, Weinberg's answer to my question can be paraphrased as:
(No answer to whether there's any interest.) As to whether the equal and opposite charge of the electron and proton can be explained, there were theories that tried to do this in the wild-and-crazy 1970's. These theories required that the gauge transformations of electromagnetism be part of a "simple" symmetry group, but none of these theories are successful ("none are well established"). And that's all I'm gonna say about it.
