RadioWeaves network operates a large number of distributed antennas using cell-free architecture to provide high data rates and support a large number of users. Operating this network in an energy-efficient manner in the limited available spectrum is crucial. Therefore, we consider energy efficiency (EE) maximization of a RadioWeaves network that shares spectrum with a collocated primary network in underlay mode. To simplify the problem, we lower bound the non-convex EE objective function to form a convex problem. We then propose a downlink power allocation policy that maximizes the EE of the secondary RadioWeaves network subject to power constraint at each access point and interference constraint at each primary user. Our numerical results investigate the secondary system's performance in interference, power, and EE constrained regimes with correlated fading channels. Furthermore, they show that the proposed power allocation scheme performs significantly better than the simpler equal power allocation scheme.