I have data on the abundance of a particular organism across a sampling area. However, instead of counts, I have the estimated biomass of the organism at at each sampling location (that is, the estimated total weight of all the organisms at that location, but not the actual number of organisms). I know that a Poisson or negative binomial model is often appropriate for count data, and the NB seems particularly appropriate for these data (the variance large relative to mean and the species is known to be spatially aggregated). Can continuous data that is really an index of of a discrete variable be modeled using a continuous distribution? I've found one or two papers where biomass data was fit to a NB distribution but they are light on details and statistical justification.

Edit: added plot of the ecdf.