This isjust a parting shot as I'm going away for a couple of weeks and all comments will be hidden until I return.
The source of energy for Bessler's wheel has to be gravity and nothing else, for some pretty obvious reasons. Bessler certainly implied that it needed only gravity, but even if you stick to the physics we have been taught, that such a device is impossible, and that Bessler was toying with us, then you need an additional force to assist the wheel to complete one rotation. So what forces are available to us?
Ambient temperature changes might have been used to make changes in the weight positions - too slow to react in my opinion and perhaps not enough of a movement to generate overbalance. Centrifugal force is another posited force but it would be difficult to regulate when to apply its theoretical movement. Magnets? Too weak and too difficult to switch on and off. Compressed air? It has to be compressed first and that would use up precious energy before it can apply itself to moving a weight. Springs? These are delayed reactions created by compressing them a some other stage in a rotation thus using up energy again. Electrostatic forces? The Leiden Jar was invented in 1745 by Dutch scientist Pieter van Musschenbroek of Leiden, who some will remember featured in my book, "Perpetual Motion; An Ancient Mystery Solved?" Again too weak a force and it would take too long to build up sufficient force to move a weight in several rotations let alone a single one.
There are others which are even weaker than those described briefly above and not readily adapted to quick or sudden requirement. In my opinion gravity-only offers the only solution and I know why it works and why it isn't impossible and why it won't make the slightest difference to the laws of physics and all of the ramifications connected to that statement.
All will be revealed upon my return - I hope ;-)
JC