The distribution of stars and gas in many galaxies is asymmetric. This so-called lopsidedness is expected to significantly affect the dynamics and evolution of the disc, including the star formation activity. Here, we measure the degree of lopsidedness for the gas distribution in a selected sample of 70 galaxies from the Westerbork HI Survey of Spiral and Irregular Galaxies. This complements our earlier work (Paper I) where the kinematic lopsidedness was derived for the same galaxies. The morphological lopsidedness is measured by performing a harmonic decomposition of the surface density maps. The amplitude of lopsidedness A_1, the fractional value of the first Fourier component, is typically quite high (about 0.1) within the optical disc and has a constant phase. Thus, lopsidedness is a common feature in galaxies and indicates a global mode. We measure A_1 out to typically one to four optical radii, sometimes even further. This is, on average, four times larger than the distance to which lopsidedness was measured in the past using near-IR as a tracer for the old stellar component, and will therefore provide a new, more stringent constraint on the mechanism for the origin of lopsidedness. Interestingly, the value of A_1 saturates beyond the optical radius. Furthermore, the plot of A_1 vs. radius shows fluctuations which we argue are due to local spiral features. We also try to explain the physical origin of this observed disc lopsidedness. No clear trend is found when the degree of lopsidedness is compared to a measure of the isolation or interaction probability of the sample galaxies. However, this does not rule out a tidal origin if the lopsidedness is long-lived. Additionally, we find that the early-type galaxies tend to be more morphologically lopsided than late-type galaxies. Both results together indicate a tidal origin for the lopsidedness.
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