Why would I need to put any weight on the pedals when the pedals themselves are balanced weight at the ends of the cranks.? Guess what, without muscle operating on them, they're not moving because the chain is holding the crank in place. Do you expect to get a perpetual motion machine? Balance has absolutely nothing to do with it. Your conception of the entire mechanism is completely wrong. We're basically walking on the pedals.

You're confounding two things here, I'm not claiming that lifting your legs provides any power to the drive train, but I'm very aware that I'm not letting my ascending leg be a completely dead weight on the pedal. I'm riding platforms, so I'm not under any delusion that doing so in any way propels the bike. Regardless, are you actually claiming that no muscular energy from either leg is expended in putting the leg back to the top? Because that's clearly a stupid assertion-leg power is the only thing advancing the chain, and if the chain doesn't advance, the crank arms don't move. I'm shocked that I'd have to spell this out to anyone who's actually ridden a bike.