So BMI = 703W/H**2.
Being thin reduces the numerator. Being tall increases the denominator.
Height actually has a greater proportionate effect. A 10% drop in weight (same height) drops the BMI 10%. A 10% increase in height (same weight) drops the BMI 21%.
Unfortunately, almost half of the presidents were 6"0" or taller. Clearly, we can rule out Taft and Trump.
I'll try George H. Bush.
George