The "center of gravity" here refers to the "weight" that "points directly at people's hearts". The fashionable saying is "ideological pressure". For students, it can probably be simply summarized by the phrase "unbearable pressure in thought".
The last sentence means: Mr. Sun doesn't want to add any psychological pressure to the students outside of study. He uses the following words to express: "You guys, you guys …", so that the whole text runs through one sentence.