Note what the FFs meant by "weakest":

...the judiciary, from the nature of its functions, will always be the least dangerous to the political rights of the Constitution; because it will be least in a capacity to annoy or injure them...It may truly be said to have neither FORCE nor WILL, but merely judgment; and must ultimately depend upon the aid of the executive arm even for the efficacy of its judgments.

~ Federalist 78

The Judiciary can only act with what the Legislature provides it and it requires the Executive to want to go along. Marbury is as good an example of this as any. In this way, the Judicial branch is still the weakest.

The biggest transformation that the FFs did not foresee is the 14th amendment, and in particular:

No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

Now, the Constitution and (in time at any rate) the Bill of Rights was something that applied to all government, state or federal, and made rights personal. The number of possible applications for judicial oversight increased astronomically, and made the federal courts in particular the natural endgame of any issue that touched on rights. And the FFs did not foresee just how far those rights would extend.

Federalist 78 also suggests a sort of sociological flaw in the Framer's thinking. When discussing the countermajoritiarian role of judges, the emphasis is on short-term madnesses that would prove self-correcting:

ill humors... which, though they speedily give place to better information, and more deliberate reflection, have a tendency, in the meantime, to occasion dangerous innovations in the government, and serious oppressions of the minor party in the community

In other words, while sudden circumstance might give rise to laws that sought to bring back the Star Chamber or take all the property of the red haired, the courts would cool the situation long enough for the mob to see the error of its ways, going on to enact rightful laws instead. There's some history as to why they thought it would play out this way (specifically, the playbook on how ancient historians like Plutarch looked at Republican Rome), but it's generally ungrounded in the way people actually behave. When there are sudden sways, the courts generally sway too, and overall are highly deferential to government as a whole. Injustices against a minority are just as often totally systemic, and take considerable weeding to get rid of rather than the speedy reassessment that seems suggested above.

So, in that the voters are much more stupid and much less stupid than the framer's thought they would act, the courts end up more at the forefront of the story, rather than the occasional aside from it.

Frankly, I think that a lot of the seeming importance of the judiciary has more to do with the fact it's the least understood.