Ralph, I think the other objects sitting on the surface are to show it is level. Also, I think you hit the nail on the head:
Your clear plastic container is cone shaped, larger circumference at the top compared to the bottom. This can obviously be seen by comparing the connecting bars between wheels 3 and 5. As it rolls it will track toward and make contact with the lid.
This may be causing rotation, the roller making its way to the lowest point in the container.
Raj. During my late night session considering your wheel:
The relative COM of the two weights will be different in water to what they are in air. Using my hillbilly math skills and your diagram in a 2d world, I used a density of 2x water for your large displacement weight, then back calculated the density of the small heavy mass, and got 35.6 x water, to be in the position you have drawn. In water, a mass with density of 1 will be neutral, so a density of 2 will have a relative weight of the water + 1, the heavier will be water + 34.6. If you then calculate the COM of these weights out of water, it will shift, causing the weights to move further right.
So, looking at the masses as density of water + "X",
the water density across the whole is the same, but with the addition of the relative extra weight, which is balanced.
The water pressure pushing down on all parts of the lower hemisphere is equal on both sides, regardless of the displacement. The masses themselves will shift to move the COM to the lowest point (balance).
Nice out of the box thinking Raj! I look forward to seeing your further testing.