There's the belief that the best way to train for a specific exercise (cycling, running, etc.) is to simply do that exercise...

Outside of just cycling more and at a higher intensity, I would say running is probably a good way to get better at cycling. It will help you lose weight, build a stronger core, increase bone density, and help your cardio/lungs. I do believe weights (i only use dumbbells or cables and workout the body from the waist up) have helped me with my cycling though. I don't do leg weights because they affect my training and if I'm cycling or running I don't need to workout the legs, already getting a good enough workout. In my prime I ran a lot, never did any other weights and was able to squat a max of 480, so I never looked at leg weights again!