The strongest legs push hardest on the pedals to make the bike move faster. Competitive cyclists train by pedaling for hours. You train for competition by taking a hard workout, feeling sore on the next day and then training at a reduced intensity until the muscle soreness disappears. Pushing heavy weights damages the muscles much more than riding long distances. Cyclists who push heavy weights with their legs take longer to recover and cannot ride as many fast miles.
Training is specific.
The best way to become strong for cycling is to ride very fast. The harder you push on the pedals, the stronger you become for pushing on the pedals. Competitive cyclists should ride very fast in short bursts called intervals once or twice a week. Lifting weights with your legs does not make you as strong for cycling as pedaling very fast. Bishop D et al.