Two-way massive MIMO amplify-and-forward relaying systems with non-ideal transceivers are investigated in this paper. To be general, multiple-antenna nodes and antenna correlation at both the user equipments (UEs) and the relay are considered, which differentiates the analysis from the prior ones. The achievable rate is analyzed and derived deterministically in closed-form. Joint scaling of the transmission powers and hardware impairments is then particularly investigated. Feasible scaling speeds for the transmission powers and hardware impairments are discovered when the number of relay antennas grows large. It is shown that down scaling of the transmission powers at the UEs and the relay and up scaling of the hardware impairment at the relay with the number of relay antennas are tolerable without reducing the expected rate. However, UE hardware impairment is a key limiting factor to the achievable rate and is not allowed to scale up with the number of relay antennas in order to achieve a non-vanishing rate. Moreover, ceiling effect on the achievable rate is still observable and the ceiling rate varies among different scaling cases. More interestingly, scalings of the UEs transmission power and the relay hardware impairment are found to be offsettable, which means that the relay hardware cost and the UE transmission power are tradable. It is found that the best tradeoff is achieved in the medium scalings of both the relay hardware impairment and UE transmission power. Numerical results are provided to verify the analysis and the tradability between the relay hardware cost and the UE transmission power. The analytical results thus provide solid foundation for flexible system designs under various cost and energy constraints.