Electro-optic modulators are essential for sensing, metrology and telecommunications. Most target fiber applications. Instead, metasurface-based architectures that modulate free-space light at gigahertz (GHz) speeds can boost flat optics technology by microwave electronics for active optics, diffractive computing or optoelectronic control. Current realizations are bulky or have low modulation efficiencies. Here, we demonstrate a hybrid silicon-organic metasurface platform that leverages Mie resonances for efficient electro-optic modulation at GHz speeds. We exploit quasi bound states in the continuum (BIC) that provide narrow linewidth (Q = 550 at lambda(res) = 1594 nm), light confinement to the non-linear material, tunability by design and voltage and GHz-speed electrodes. Key to the achieved modulation of Delta T/T-max = 67% are molecules with r(33) = 100 pm/V and optical field optimization for low-loss. We demonstrate DC tuning of the resonant frequency of quasi-BIC by Delta lambda(res) = 11 nm, surpassing its linewidth, and modulation up to 5 GHz (f(EO,- 3dB) = 3 GHz). Guided mode resonances tune by Delta lambda(res) = 20 nm. Our hybrid platform may incorporate free-space nanostructures of any geometry or material, by application of the active layer post-fabrication.