The effects of a density asymmetry across the current sheet on anti-parallel magnetic reconnection are studied systematically in a laboratory plasma. Despite a significant density ratio of up to 10, the in-plane magnetic field profile is not significantly changed. On the other hand, the out-of-plane Hall magnetic field profile is considerably modified; it is almost bipolar in structure with the density asymmetry, as compared to quadrupolar in structure with the symmetric configuration. Moreover, the ion stagnation point is shifted to the low-density side, and the electrostatic potential profile also becomes asymmetric with a deeper potential well on the low-density side. Nonclassical bulk electron heating together with electromagnetic fluctuations in the lower hybrid frequency range is observed near the low-density-side separatrix. The dependence of the ion outflow and reconnection electric field on the density asymmetry is measured and compared with theoretical expectations. The measured ion outflow speeds are about 40% of the theoretical values.