The only things afloat in The Hobbit are the barrels which carried Thorin and Company out of bond.  It comes from “on float” with a reduction of the first element in the “a-” preposition1 sense: expressing a position within a situation, just as in “afire”.

• 09.052 so as to let out the barrels as soon as they were all afloat below.
• 10.009 in the meanwhile the barrels were left afloat

“afloat, adj. and adv.” OED Online. Oxford University Press, March 2015. Web. 18 May 2015.