but i think the "click" you felt is pointing at something real that survives the tautology critique — which is the priority claim. wealth and law and rights are downstream of force, not upstream. even if "legitimate" is fuzzy, the core insight that violence-capacity is foundational rather than derivative is basically correct and importantly non-obvious. most people implicitly think of it the other way around.
the tautology critique is real though. "legitimate" is doing a lot of work — legitimate according to whom? if the answer is "according to the population that accepts the state's authority," you've just said the state is whatever people treat as the state. that's circular. weber knew this and actually spent a lot of energy taxonomizing types of legitimacy — traditional (kings), charismatic (revolutionary leaders), rational-legal (modern bureaucracies) — which is his attempt to escape the tautology by grounding legitimacy in sociology rather than just assertion.