Sir Richard,
"Heavier aircraft (of the same type) glide further than lighter aircraft as they start with a higher total energy."
Not true I'm afraid.
Best glide range is achieved at the optimum lift/drag ratio. The heavier aeroplane will maintain exactly the same lift/drag ratio as the lighter one provided that speed is increased.
Therefore, providing the aeroplane is flown at the correct speed for the weight, glide range will not be affected by weight.