The dosage of a cold medication is 2 mg for every 80 lb of body weight. How many milligrams of this medication are required for a person who weighs 140 lb?

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}