I have trouble in this sentence.

With the loosening of familiar obligations came unprecedented opportunities for personal autonomy and voluntary choice. Massachusetts inaugurated a new era of religious pluralism in 1834, ending two centuries of mandatory support for local churches. Even in Concord, a slim majority approved the change, and as soon as it became law, townspeople deserted the two existing churches—the Unitarian flock of the Reverend Ripley and an orthodox Calvinist congregation founded in 1826—in droves. The Sabbath no longer brought all ranks and orders together in obligatory devotion to the Word of God. Instead, townspeople gathered in an expanding array of voluntary associations—libraries, lyceums, charitable and missionary groups, Masonic lodges, antislavery and temperance societies, among others—to promote diverse projects for the common good. The privileged classes, particularly the village elite, were remarkably active in these campaigns. But even as they pulled back from customary roles and withdrew into private associations, they continued to exercise public power.

I can't understand, what's meaning of "a slim majority approved the change"? A small majority? It's so werid. Can the number of a group become both the majority and small?
Thank you very much!