If my neighbor (whom I have allowed to connect to my router) is sharing my internet via Bluetooth tethering, is there a way to prevent anyone else from sharing my internet via his or my Bluetooth without cutting him off?
Basically, anyone allowed to connect to your router/wifi access point can in turn make their computer (or whatever device) into a router of their own. They can then, without your router even knowing, create their own little network and share internet amongst themselves, then relaying the traffic through one device.
You can generally see what devices are connected directly to your router from its administration page, but this will not show ones that are connected via bluetooth tethering or some other means, thus relaying through a device that does show up in the list.
Unfortunately, there's no easy way on a home router to prevent this type of thing. I think the best approach might be to talk to him and ask him if he's doing that, and negotiate a solution.
Bluetooth does not create a strong internet signal so anyone connecting to it would have to pair to his device that is tethered. They would have to be in a 60 foot radius of that device in most cases. I don't think there is anything on your home consumer based router that will allow you to block him. Since he connects the Bluetooth device to the computer he is connected to your WiFi, and the traffic is routed through is laptop to his device. Filtering will not really work since the table will not show the MAC address of the device that is tethered.
Either way the distance is a major factor even so the max transfer rate in best case situations is only 24MB/s. As the device gets further away the signal degrades.