Final answer:
Interest groups formally weigh in on Supreme Court decisions by filing amicus curiae briefs, which are legal documents that present their positions to the Court.
Step-by-step explanation:
The formal method by which interest groups attempt to influence Supreme Court decisions is by filing amicus curiae briefs. These 'friend of the court' briefs are legal documents that allow interest groups, who are not direct parties to a case, to present their viewpoints to the justices. Through these briefs, groups can provide the Court with additional information, insights, or arguments that may affect the justices' decisions on cases that bear on their interests.
Amicus curiae briefs are intended to influence the Court's decision by presenting legal arguments and showing how the decision may impact the general public or a specific population.For instance, in landmark cases such as Obergefell v. Hodges or Sierra Club v. Trump, numerous interest groups submitted amicus briefs to express their stakes in the outcome and to try to steer the Court's verdicts in their favor.