  Weighted group algebras have been studied extensively in Abstract Harmonic
Analysis where complete characterizations have been found for some important
properties of weighted group algebras, namely amenability and Arens regularity.
One of the generalizations of weighted group algebras is weighted hypergroup
algebras. Defining weighted hypergroups, analogous to weighted groups, we study
Arens regularity and isomorphism to operator algebras for them. We also examine
our results on three classes of discrete weighted hypergroups constructed by
conjugacy classes of FC groups, the dual space of compact groups, and
hypergroup structure defined by orthogonal polynomials. We observe some
unexpected examples regarding Arens regularity and operator isomorphisms of
weighted hypergroup algebras.
