Hi Chris,
Sorry to hear this.* I had a similar situation with an ornamental cherry I inherited with the house.* The roots of trees grow beyond the outer dripline of the canopy.* In our case we severed the roots where they went under the deck and left them to rot.* Here's info on how tree roots grow.
http://edis.ifas.ufl.edu/pdffiles/MG/MG08900.pdf
http://edis.ifas.ufl.edu/WO017
http://www.ext.colostate.edu/pubs/Garden/02926.html
http://www.treesaregood.com/treecare/trees_turf.aspx
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.