The 'weave mode' in your "wagon steering" wagons has several contributing factors, but the principle ones are front AND rear toe alignment and tire properties. Folks generally don't put the best tires on these rigs (and seldom check the pressures), but the best tires are radials running at their highest rated tire pressure. This is because the tires have a restoring self aligning moment ('twisting force') when the axle turns. This moment takes some time/distance to act on the axle, and this delay causes the chassis to weave. So, higher pressure lowers the self aligning moment, radials have less self aligning moment characteristic than bias tires and the speed at which the weave tends to start goes up. Another thing I've observed is the beam connecting the rear axle to the front gets bent downward from overloading the wagon. This increases the net caster alignment of the front axles and caster generates higher self aligning moment (which adds to the problem).