Tikkun Olam, literally “fixing the world”, is a term that originates (as far as I’m aware) in the Gemara’s re-telling of the story about how Hillel created the concept of a pruzbul as a “tikkun olam”, so that people would not violate the prohibitions related to Shivyis. Somehow, I doubt that the “tikkun olam” that Weiss is referring to has anything to do with making sure people don’t sin.
(And as a side point, I don’t think it’s accurate to refer to Weiss as an MO Rabbi. Although he does try to claim this title, his beliefs are far out of the pale of Orthodoxy, Modern or not.)