The phrase seems to be of Scottish origin. As Hugo found, most of the earliest uses of the phrase have to do with alcohol consumption. I did find this earlier figurative use of the phrase however from *[The History Of The Church And State Of  Scotland][1]*, 1753 ([date check][2]):

![http://books.google.com/books?id=mQM-AAAAcAAJ&q=mdccliii#v=snippet&q=belt&f=false][3]

It appears the figurative sense of _under one's belt_ to mean owned or "contained by" goes back even further as evidenced by this old Scottish saying from *[A Complete Collection of Scotish Proverbs][4]*, 1721:

![enter image description here][5] 


  [1]: http://books.google.com/books?id=mQM-AAAAcAAJ&q=mdccliii#v=snippet&q=belt&f=false
  [2]: http://books.google.com/books?id=mQM-AAAAcAAJ&q=mdccliii#v=snippet&q=mdccliii&f=false
  [3]: https://i.sstatic.net/Y3NFd.png
  [4]: http://books.google.com/books?id=BEgOAAAAQAAJ&pg=PA246&dq=%22under%20*%20belt%22&hl=en&sa=X&ei=DCO-T-udHPHgsQLR6vQb&ved=0CFAQ6AEwBDgK#v=onepage&q=%22under%20*%20belt%22&f=false
  [5]: https://i.sstatic.net/MRon5.png