Ceremonial scepters are the most apparent insignia of rulership, the ultimate symbol of authority. The weighty baton might have been carried horizontally as an 'offering bundle', see Olmec Art, pl. 117.
Such Olmec figural ceremonial scepters are extremely rare, for one other extant example see Joralemon, fig. 10p.
Cf. Olmec Art, pl. 104, for a smaller version.