It is, very weird.....I only could understand it's weirdness when I met "ja" and "doch" in German. (Although I cannot say that mesmo is equivalent to "ja" - because I just don't understand "ja" yet - I'd risk saying there is some resemblance....or maybe doch?)
In this case, and lots of other cases "mesmo" works as an "assurance" word. It adds an idea that he doesn't brake or doesn't need to brake anywhere else, but "aí mesmo" is ok.
So this "mesmo" is like assuring that it's nowhere/nothing else, as if there is or would be a question about the place.
This case can also be seen in contructions like "ele mesmo vai...." (he goes himself - not anyone else...)