Weighted k nearest neighbor search
As per @an6u5's comment:
If you want to weight one dimension higher than others then I suggest you standardize all of your data so that the mean is zero and the standard deviation is one. Then you can multiply the less important dimensions by a factor (2-10) so that they appear farther away to the KNN distance metric and leave the most important dimension un-scaled. Note that both standardizing and scaling are completely reversible processes, so there is very little reason not to use this simple solution