Changing hit weights moves the checked centroid marker. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Left weight pulls the centroid left
Weights 3 and 1 on positions 2 m and 6 m give numerator 12 and total weight 4.
xc=12/4=3
Right weight pulls the centroid right
Weights 1 and 3 on positions 2 m and 6 m give numerator 20 and total weight 4.
xc=20/4=5
Equal weights center the marker
Weights 2 and 2 on positions 2 m and 6 m give numerator 16 and total weight 4.