It is interesting to note the way the question was worded. The idea of "danger" and "strength" seem to be converged in a unique manner. I would not say the judiciary is the weakest of the three branches. It is true that the framers did not confer much in the way of specific powers to it, but it holds tremendous persuasion in its ability to strike down laws or actions deemed unconstitutional. Throughout the history of the nation, the Supreme Court and the judicial branch have been responsible for some of the most powerful and pressing issues have been ruled on by the judicial branch. The start of the nation's Civil War was brought on by the Dred Scott decision, racial segregation practices were both upheld and overturned by the court in Plessy v. Ferguson and Brown vs. Board of Education. The case of Roe v. Wade helped to define the critical issue of abortion, creating a litmus test that has been in American politics for the last 40 years. Finally, in the ultimate act of definition of power, the judicial branch decided the outcome of a presidential election in the 2000 case Gore v. Bush.
The judicial branch is not necessarily weaker than the other branches because Hamilton called it "the least dangerous branch." Perhaps Hamilton felt it is the least dangerous of the three branches of government because it does not make the laws as the legislative branch does; it simply interprets the laws that have been passed by the legislative branch and that have been approved by the executive branch.
Dangers enter into the law-making process because congressmen can be pressured by their constituents, lobbyists, and powerful people to write laws or vote for laws that are against the dictates of their consciences. Or they may wish to include in bills things that will enable them or their constituents. At any rate, there may seem to be more opportunities for corruption in both the legislative branch and the executive branch in lawmaking than in the judicial branch's interpretation of these laws.
The legislative branch is designed to manage conflict over interpretation, application, or enforcement of laws whereas the legislative branch can be embroiled with such conflict--a more dangerous situation.
The US Constitution divides the responsibilities and duties of the government into three separate branches. One is not more powerful nor less powerful than the other. The system of the three branches consists of checks and balances or limits imposed on each branch through checking by the other branches.
The Legislative branch, elected members of congress, write laws that are checked by the Judicial branch, or Supreme Court. The legislative branch can also check the judicial branch by enacting other laws. The Executive branch, the president and vice-president, whom make sure that laws are obeyed are checked by the legislative branch, through the veto override process, and also by the Judicial branch.