It's not a weakness. Empathy is literally the emotion on which all of civilization is built. Civilization was not built, and never could be built, by a bunch of atomized individuals. It was built out of shared identity, which is a function of empathy. Once civilization got going, there were plenty of developments like slavery -- but still, empathy is the basis of a community or even a nation.
Your views are loathsome and disgusting. Empathy is the most powerful emotion. It is not a weakness at all; it takes great strength. And our best presidents have typically been motivated by empathy (see, e.g., Lincoln, FDR, Obama), an dour worst presidents the ones who preached individualism or mindless tribalism (Hoover, Coolidge, Nixon, Trump). This isn't a close call.