Weinberg doesn't make a convincing case for the existence of a final theory. Indeed, given the very title of the book, one doubts that he has any strong belief that it can be found. In building up the case for a final theory, Weinberg canters through a history of modern physics, culminating in an account of his electroweak theory, symmetry breaking, and string theory. But he goes through this material far too quickly for anyone to get a good grasp of them, excepting perhaps theoretical physicists working in the field.
Until the penultimate chapter I was tempted to give the book only two stars, but that chapter is so good I decided to double the star rating. I have never read a more intellectually honest, indeed brutal, defence of atheism, or a better account of the (non-)spirituality of science.
Weinberg's honesty comes from a blunt admission that he doesn't find that science provides spiritual satisfaction, thereby undermining the simple sentimentaility of the Brian Cox "it's wonderful!" brigade. I have a degree in physics and never saw black holes or quantum experiments as more than "mildly interesting", like the solution to a good chess problem. So it's good to see a physicist of the highest standing underwriting my feelings!
The message of chapter XI is so bleak - there's no God and science does not provide spiritial satisfaction - that I think Weinberg should have provided some hints as to where at least some kind of satisfaction might be found. Schopenhauer is equally bleak, but even he points to contemplating great works of art as allowing us to escape from the unsatisfied will.
If you are feeling depressed after reading Weinberg try reading
The How Of Happiness, where the author gives an account of enjoying teaching her son mathematics, and enjoying doing statistical analyses, that indicates the kind of satisfaction that science can bring - not spiritual, but at least the 'ego escaping' kind of satisfaction that Schopenhauer is talking about.
This is definitely a book that everyone should read, if only for chapter XI. Any physicist tempted to jump on the popularising bandwagon should read chapter X1 four times before doing so.