This is a science book for the masses, focused on the first three minutes of the universe. For the first half I was able to follow along, but the technical detail ramps up quickly, and it spends quite a few pages on proving the result and covering the history of the research. Weinberg makes it clear that he’s writing for a reader with some mathematical chops, and there are a few attempts at mass-market appeal, like the use of ‘100 million’ instead of scientific notation, but other stumbling blocks are pretty much unchanged, like an understanding of quantum particles.
If you’re motivated to understand this area of astrophysics, this might be a good place to start, though it has probably been overshadowed by a more recent book. If you’re looking for a casual read, this isn’t it.