The grading vocabulary is worth understanding because it is often misread from outside. Sound, good and weak describe the chain of transmission, not the content: whether the transmitters were reliable, whether they can be shown to have met, whether the chain is unbroken back to a companion. A weak report is not a report judged false; it is one whose transmission cannot be established to the required standard, and jurists differ on what may be done with such material, with some allowing it for moral encouragement and not for law. Al-Tirmidhi notes on which school used which report make his collection a source for the history of that disagreement as well as a repository.
His other well known work belongs to a different genre altogether. The Shama'il gathers reports about the Prophet appearance, dress, manner of walking, eating, sleeping and laughing, and it is read devotionally rather than legally. Books of that kind sustain a whole tradition of emulation in daily habit, and the fact that the same compiler produced both a lawyer reference and a portrait for imitation is a useful reminder that hadith literature was never a single kind of writing.
There is a limit worth stating. Criticism based on the chain can establish that a report was transmitted carefully and cannot establish that the event happened, and the tradition is aware of this: the machinery was built to control transmission at a moment when reports were multiplying, not to settle history in the modern sense. Academic study of hadith asks a different question with different methods, and reads the same collections as evidence about the communities that assembled them.