Apparently the Old English meaning of “overhear” was to not pay attention to something you heard, as in “disobey”.  Our hobbit is the only character who overhears in the novel, by the modern usage “to hear without the speaker intending you should do so”.

• 01.097 if I have overheard words that you were saying.
• 09.013 to overhear some of the guards talking
• 19.006 for he overheard the words of the wizard to Elrond.

“over-, prefix.” OED Online. Oxford University Press, June 2015. Web. 14 July 2015.

“overhear, v.” OED Online. Oxford University Press, June 2015. Web. 14 July 2015.