If by "put their entire weight," you mean: "fulfill the law perfectly," Paul very specifically disputes the Jewish understanding of salvation by declaring that the unrighteous are justified and have their sins forgiven them through no obedience or merit of their own, but by faith only.
Exactly. The object of faith became Christ, not a set of rules. However, that faith, in the Hebrew mind, was a meaningless concept apart from “works”, that is, obedience. To a Hebrew, right response (obedience) trumps right understanding (systematic theology, even biblical systematic theology).
Justification would be a meaningless concept without the works that go along with the new status. The argument about which comes “first”, or which was more “essential”, would be foreign concepts to Jesus or the writers of the New Testament.
I like theology and counting verses and stuff like that. But I realize that it is strictly an organizing tool, and not the truth in itself.