In short, Burr was from New York, where dueling was already a practice on 'the outs', and the demise would be further spurred along by the result of Hamilton's fatal end. Had he been from the South, perhaps it wouldn't have been such a blow to his political career, as a number of Southern politicians engaged in duels without any particular ill-effect on their fortunes. For a more in-depth discussion of the social ramifications of dueling in the period, I would direct you to the Hamilton AMA from last year, as I wrote at length about the duel, and dueling in the period.