Standardize same-scale variables?
It is better to standardize the data even though being on same scale. Standardizing would reduce the distance (specifically euclidean) that would help weights to not vary much from the point intial to them. Having huge seperated distance would rather have more calculation involved. Also distance calculation done in KNN requires feature values to scaling is always prefered.
thinking about a problem… should you standardize two predictors that are already on the same scale (say kilograms) but may have different ranges? The model is a KNN
I think you should because the model will give the predictor eith the higher range more importance in calculating distance