Marihuana Control Act of 1979 - Amends the Controlled Substances Act to establish a civil fine of not more than $100 for anyone who: (1) possesses not more than one ounce of marihuana within a private dwelling for his or her own use, or for the use of others within such dwelling, if it is not possessed with the intent to distribute, transfer, or sell in violation of Federal law; (2) possesses in a public area not more than one ounce of marihuana incident to a private use, if it is not possessed with the intent to distribute, transfer, or sell for profit in violation of Federal law; or (3) distributes or transfers lawfully possessed marihuana in public or private to any person for a lawful private use, if such distribution or transfer is not made for profit.