It's not true all the time, just pootling along at 10mph there won't be any difference at all.
But if you ever get out of the saddle (or push down hard enough on the pedals that the effective weight on the saddle is nothing) then you'll be getting the benefit of the extra weight. Yes you will work harder (since you have to lift your CoG back up to the top of the pedal stroke, which is now more work because of the extra weight), but the point is that you can put more downward force through the pedals because of the extra mass. More downward force available = faster.
The m in F=ma (for the entire bike) remains the same, but the F (pedal force) will be greater because of the increased mass of the rider.
It's not magically making you faster, it's just a device to allow you to extend beyond an existing limit (of downward pedal force) bounded by your physical mass. Much like a bicycle doesn't provide any energy itself, but it allows me to cover ground much faster and more efficiently than I'm able to even when sprinting.