I'm not a ham. I have no real experience doing what you are looking to do. But I have read some about this and I think I might be able to steer you in the right direction at least form what I understand. The Kenwood radio that you have has a built in TNC I believe. Therefore you don't need something to output in Peet Bro's format out of WeeWX but rather all you need is WeeWX to understand how to talk to your radio's TNC in a format that it accepts. Perhaps that is the same thing as Peet Bro's output.
I think the integration you need is WeeWX --- to ---> TNC
..and I believe that is possible with APRX extension:
Hopefully this gets you close to your objective.