categories: Weighted limits

[Mark Hovey <hovey@picard.math.wesleyan.edu>]

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