The legislative branch of the US was created as the first of three branches of the government. That is why its powers are defined in Article I of the US Constitution. Though there are three branches in the federal government, and they were created as equal in power, the members of the US Congress nevertheless carry with them a closer proximity to the people, and a closer kinship with the people, they serve as with regard ideas and legislation.
Members of the House of Representatives are elected every two years, and senators every six (there are exceptions). The number of representatives in each state is determined by population, and these officials represent districts, while senators are two each for every state and represent the entire state. One can see a possible weakness here: Why would a state with a large population, like California, have the same amount of senators as Wyoming, a state with a small population? Is this fair? Some would argue that this is unfair.
That, according to many in the US, is a weakness in the legislative branch of government. And if one understands the Electoral College Presidential Election system in the US, as many do, then it is easy to understand why it is partially for this reason that loud voices cry out every election season that elections in the US are not "one person, one vote."
So, if one analyzes how some legislators are apportioned, and how that apportionment affects the people those legislators serve—as well as presidential elections—then the legislative branch of government could be seen as flawed and thus a weakness.