If someone slandered you and tried to cover it up wouldn't you think that a lawyer or judge should not require proof if you tell him or her that the person will try to cover it up to seem as if there is no slander or anything else, but continue to do it?
No, I would not think that.
If they don't look into it what is to keep the person from continuing it.
I'm not sure who "they" are in this sentence, but context seems to indicate that "they" are the lawyer and judge to whom you referred in the prior sentence. If so, judges do not "look into" things. Judges are essentially referees. They will make rulings based on evidence brought before them. If there is no jury, then the judge will ultimately determine if the parties have or have not proven their claims. Lawyers will "look into" things. If you go to a lawyer and claim that "Bob slandered me and I want to sue," the lawyer will sit down and discuss your allegation. If the lawyer believes you have a good case, he/she may agree to represent you, in which case he/she will help you gather the evidence you need to try and prove what you claim.