I found nothing on Mary Ann Morgan Looney, prior to 1850 census. Some lines had her marrying Arthur on Oct 10, 1816, but I didn't find it in the available Hawkins Co, TN records. I did find one thing to add for your research:
Arthur's pension, Mary Ann listed as getting in 1871
War of 1812 Pension Application Files Index, 1812-1815 for Arthur G Looney
Loo - Ly
Sorry I couldn't be of helpt