Given that the dosage of the cold medication is 2 mg for every 80 lb of body weight.
Let x be the amount of medication required for a person who weighs 140 lb.
Using the proportion method:
\dfrac{2 mg}{80 lb} = \dfrac{x mg}{140 lb}
Solving for x:
x = \dfrac{2 mg}{80 lb} \times 140 lb
x = 3.5 mg
Therefore, for a person who weighs 140 lb, 3.5 mg of the medication are required.
\boxed{3.5 mg}