Weighted limits

What are the standard references for weighted limits and colimits in enriched categories? I know about Borceux, volume 2, chapter 6, but that does not go far enough. More precisely, I want to know how functorial the weighted colimit is in the weight. Given a V-natural transformation F --> F', presumably I get some kind of map from colim_F G to colim_F' G (or the other way around). I would like a reference for this fact and related functoriality facts. Presumably the weighted colimit is a bifunctor in the weight and the functor one is taking the colimit of, and presumably this bifunctor has various good properties. Has anybody ever written these down? Thanks in advance for any help you can give me. Mark Hovey