Here is the solution if the unique weight is number 8 and it is Heavier
than all others, followed by solution if it was Light.

Weigh #1

Place 1 2 3 4 on Left and Place 5 6 7 8 on Right
Solver now knows Unique Weight is either 1 2 3 4 as Light OR 5 6 7 or 8 as Heavy

Weigh #2

Place 1 2 6 on Left and Place 3 4 5 on Right

So Unique weight must be either 7 or 8 as Heavy

Weigh#3

Place 7 on Left side and place 8 on Right side

Solver would see that Right is Heavy so it is 8 Heavy

***********

Now assume instead that 7 is Light instead of Heavy.

Weigh#1

Place 1 2 3 4 on Left and Place 5 6 7 8 on Right

Either 1 2 3 or 4 is Heavy Or 5 6 7 or 8 is Light

Weigh#2

Place 1 2 6 on Left and Place 3 4 5 on Right

Solver would see that scale is in balance so it must be either 7 or 8 is Light

Weigh #3

Place 7 on Left Place 8 on Right

Solver would see that Right side is Light so Unique weight is 8 as Light

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