How can I increase the towing capacity of my 1980 Jeep CJ-7?

short answer, you can't. towing capacity is determined by such a large combination of things including, but not limited to engine torque, transmission strength, axel strength, gear ratio, braking power, frame strength, and suspension design. The factory listed towing capacity is determined by the weakest link in that chain of parts. The weakest link for every vehicle is different, and even if you could fix the weakest link, the next weakest link in the chain won't be far behind. So you could rebuild everything in your Jeep, put in a diesel, modify a fully-floating rear axle housing for your jeep, upgrade your transmission etc. Even if you did all these things determining the "new" towing capacity would be impossible, although you could undoubtedly pull more, you wouldn't know your limit. And this would cost you tens of thousands of dollars. Also, wheel base plays a large part in towing safely, longer wheel base vehicles tow much better and handle with larger loads. The jeep is about as short a wheelbase as you can get, so towing a trailer of any size would get squirly quick. Your best bet it to save up $1500 and buy a used 3/4-ton or 1-ton truck for your pulling needs. A jeep is not a towing vehicle, period.