Beilinson's original paper on Height pairingsBeilinson's original paper on Height pairings does indicate how his height pairing generalises that of Neron-TateNéron–Tate: see page 10 (also, MullerMüller-Stach and Kunneman's works expand on Remark 4.0.8 on page 14). Also, Scholl's paperScholl's paper provides a very nice interpretation (via Ext in mixed motives).