Tunneling spectroscopy of InAs nanocrystals deposited on graphite was measured using scanning tunneling microscopy, in a double-barrier tunnel-junction configuration. The effect of the junction symmetry on the tunneling spectra is studied experimentally and modeled theoretically. When the tip is retracted, we observe resonant tunneling through the nanocrystal states without charging. Charging is regained upon reducing the tip-nanocrystal distance, making the junction more symmetric. The effect of voltage distribution between the junctions on the measured spectra is also discussed.