I have Chinese Elms, also called Syberian Elms, all over my yard. In fact I just cut one down a few weeks back. They are useless trees. You can try to burn it for camp wood but DO NOTuse it in your smoker or indoor fireplace or wood stove. It can be used in outdoor furnaces.
As you said it is heavy, this is due to a high sap content. Once it drys it is like balsa wood. When you burn it the smell is like urine. Stay upwind!