Free-space optical (FSO) communications are becoming promising schemes for high-capacity wireless links due to their plentiful characteristics originated from higher carrier frequency. These characteristics also yield a greater security advantage over radio frequency counterparts: the physical ability of a wiretapper is reasonably restricted due to the high directionality of communication beam and the line-of-sight configuration of the link. Secret key agreement over FSO links (FSO-SKA) employs this security advantage as well as the post-processing over an authenticated public channel to establish an information-theoretic secure key which cannot be broken even with unbounded computer resources. In the previous works, the authors demonstrated the full-field implementations of FSO-SKA with a 7.8-km FSO link testbed including a probing station to estimate the possible wiretapping risks from the sidelobe of the communication beam. In the demonstration, however, there is still room to improve the secret key rate by exploiting the optical fading which contains additional information about random states of the FSO links. We here propose a novel protocol for FSO-SKA employing such channel state information. In the protocol, the legitimate receiver decides whether to discard the received symbols or not according to the received optical power at the time. Based on the experimental data from the FSO link testbed, we demonstrate that the proposed protocol improves the secret key rate compared with our previous result. To our best knowledge, this is the first demonstration that exploits the effect of atmospheric turbulences to improve the security performance of communication systems. We anticipate that this idea will be applicable on the broader areas of FSO communications and opens a way toward practical wireless network spanned by FSO links.