Is there a machine learning algorithm that does what I describe? (See text)

While reading a textbook on data mining, I had an idea for an algorithm: it'd work like KNN, except that instead of averaging the 'K' nearest neighbors to estimate the response variable, all neighbors are weighed according to 1) their distance and 2) importance of the X variables (e.g. if X2 is more correlated/valuable than X1, distances among neighbors' X2 variables are weighed more heavily than X1).

I'm sure this already had been thought of, so what family does something like this belong to?