In this joint work with Armin Rainer (University of Vienna) we have characterized the validity of the Whitney extension theorem in the ultradifferentiable Roumieu setting with controlled loss of regularity (mixed setting). We have considered classes defined in terms of so-called Braun-Meise-Taylor weight functions. This is a continuation of a very recently published article with title "On the extension of Whitney ultrajets". On the one hand we have been now able to get rid of an undesired assumption in the main theorem of this first work. On the other hand we have answered several further questions stated there and have obtained a more complete characterization of stability properties for ultradifferentiable classes defined by weight functions.