We present multi-epoch continuum observations of the Class 0 protostellar system IRAS 16293-2422 taken with the Very Large Array (VLA) at multiple wavelengths between 7 mm and 15 cm (41 GHz down to 2 GHz), as well as single-epoch Atacama Large Millimeter/submillimeter Array continuum observations covering the range from 0.4 to 1.3 mm (700 GHz down to 230 GHz). The new VLA observations confirm that source A2 is a protostar driving episodic mass ejections, and reveal the complex relative motion between A2 and A1. The spectrum of component B can be described by a single power law (S _ν ∝ ν ^2.28) over the entire range from 3 to 700 GHz (10 cm down to 0.4 mm), suggesting that the emission is entirely dominated by dust even at λ = 10 cm. Finally, the size of source B appears to increase with frequency up to 41 GHz, remaining roughly constant (at 0.″39 ≡ 55 au) at higher frequencies. We interpret this as evidence that source B is a dusty structure of finite size that becomes increasingly optically thick at higher frequencies until, in the millimeter regime, the source becomes entirely optically thick. The lack of excess free-free emission at long wavelengths, combined with the absence of high-velocity molecular emission, indicates that source B does not drive a powerful outflow, and might indicate that source B is at a particularly early stage of its evolution.