unfortunately not a statistics phd :/
However, why not just sample from the empirical distribution, and bootstrap for asymmetric (if the distribution is asymmetric) confidence intervals?
But I like the regression approach more, I think it would be very feasible to predict weight from what people have bought, e.g., rick owens is negatively correlated with weight, EG interacts with race, so if you are white and buy EG, you are on the heavy side, if asian, less so?