By the work of Richard Hain, the archimedean height pairing on ordinary algebraic cycles can be interpreted as an invariant of an associated mixed Hodge structure. In this talk, we will present a similar construction for higher cycles in the Bloch complex. Families of higher cycles produce admissible variations of mixed Hodge structure. We will describe the asymptotic behavior of the height pairing in the case where the associated variation of mixed Hodge structure is Hodge-Tate. This is joint work with J. Burgos Gil and S. Goswami.