What does "minimum stability" mean? I don't think it means anything. A ship will never weigh less than its light ship weight (except perhaps at the time of launch and a few days after) and will never weigh more (it should not) than at maximum design load condition. Stability, regardless of the parameter that is taken to measure it, is usually greater in the condition of light ship weight. But it all depends on how you measure stability, be it the maximum or the minimum.
If we study the limit KG curve, it is usually a decreasing ordinate curve (KG value) as the abscissa (displacement) increases. If we take the KG value as a measure of stability, stability decreases with displacement.