  We introduce and study smooth compactifications of the moduli space of n
labeled points with weights in projective space, which have normal crossings
boundary and are defined as GIT quotients of the weighted Fulton-MacPherson
compactification. We show that the GIT quotient of a wonderful compactification
is also a wonderful compactification under certain hypotheses. We also study a
weighted version of the configuration spaces parametrizing n points in affine
space up to translation and homothety. In dimension one, the above
compactifications are isomorphic to Hassett's moduli space of rational weighted
stable curves.
