Let P be a partial order on [n] = {1,2,...,n}, Fqnbe the linear space of n-tuples over a finite field Fqand w be a weight on Fq. In this paper, we consider metrics on \mathbb Fqninduced by chain orders P over [n] and weights w over \mathbb Fq, and we determine the cardinality of all optimal anticodes and completely classify them. Moreover, we determine all diameter perfect codes for a set of relevant instances on the aforementioned metric spaces.