Plasmons are collective oscillations of mobile electrons with dynamics controlled by their charge stiffness (“Drude weight”). Using terahertz spacetime metrology, we probe plasmon dynamics of mono- and bi-layer graphene. In both systems, the experimentally measured Drude weight systematically exceeds the prediction based on a noninteracting electronic system. The enhancement of the spectral weight is most prominent in vicinity of charge neutrality. We attribute the observed spectral weight anomalies to the interplay of Coulomb interactions and the wavefunction geometry of graphene bands. Our results establish that the interplay of quantum geometry and interactions can directly influence collective excitations, with implications that extend beyond graphene to a broad class of quantum materials.