Judicial review was invented by Federalists specifically to subvert Jefferson really. It's in some sense an antidemocratic institution.
Judicial review is simply the concrete manifestation of two things express in the Constitution:
(1) the judicial power regarding cases and controversies arising under the Constitution, laws, etc., and
(2) The Constitution’s express limits on what laws Congress has the power to pass.
It's anti-democratic in the sense that Constitutionally-limited government is itself anti-democratic, in that the electre representatives of the people are denied the unlimited power they would have in a parliamentary supremacy model, but not in any other sense.