We optimize secret key rates (SKRs) of weak coherent pulse (WCP)-based quantum key distribution (QKD) over time-varying free-space optical channels affected by atmospheric turbulence. The random irradiance fluctuation due to scintillation degrades the SKR performance of WCP-based QKD, and to improve the SKR performance, we propose an adaptive scheme in which transmit power is changed in accordance with the channel state information. We first optimize BB84 and decoy state-based QKD protocols for different channel transmittances. We then present our adaptation method, to overcome scintillation effects, of changing the source intensity based on channel state predictions from a linear autoregressive model while ensuring the security against the eavesdropper. By simulation, we demonstrate that by making the source adaptive to the time-varying channel conditions, SKRs of WCP-based QKD can be improved up to over 20%.