Experimental and theoretical studies of the effects of weak radio-frequency electric fields on Rydberg-Stark states with electric dipole moments as large as 10,000 D are reported. High-resolution laser spectroscopic studies of Rydberg states with principal quantum number n = 52 and 53 were performed in pulsed supersonic beams of metastable helium with the excited atoms detected by pulsed electric field ionisation. Experiments were carried out in the presence of sinusoidally oscillating electric fields with frequencies of 20 MHz, amplitudes of up to 120 mV/cm, and dc offsets of up to 4.4 V/cm. In weak fields, the experimentally recorded spectra are in excellent agreement with the results of calculations carried out using Floquet methods to account for electric dipole couplings in the oscillating fields. This highlights the validity of these techniques for the accurate calculation of the Stark energy level structure in such fields, and the limitations of the calculations in stronger fields where n-mixing and higher order contributions become important.