You guys are looking at this all wrong. Yeah, weights seem like the perfect solution, but on the downward stroke they're only making use of the standard, everyday acceleration of gravity. To really capitalize on this revolutionary idea, you need to use springs which cause a downward acceleration and exceleration. See F=ma=kx, so you only need to find springs with a spring constant, k=ηma/x, where η is any number greater than 1 and is the pedaling efficiency factor. So, if you want your pedaling to be 20 times more efficient than it is now, you need to buy springs with k=20ma/x, where x would be 2 times your crank length, m is the mass of the pedal/foot system, and a is your local acceleration of gravity. Obviously this will increase your acceleration, and by improving your efficiency, it thusly increases your exceleration (the rate at which your cycling increasingly excels).
Note: all claims herein are theoretical in nature and not a guarantee of actual results. No animals were harmed in testing, and all test subjects were monitored and observed using unobjective methods. Biomechanical claims are made without any knowledge of biomechanics whatsoever. All rights reserved.