I'm not convinced that you have a normal 2 mixture distribution, maybe 3 mixture? But probably not. I'd check for rounding in your measurements to see if thing gets rounded to 0.1, 0.2, 0,25, and 0.35. Those values seem to occur more often.
Try using the SHASH distribution model. The goodness of fit is available for that model
Distribution models with more parameters can account for asymmetry and weird tails better than simpler models.
Mixture distributions don't have goodness of fit, because which fit would you be evaluating?
JMP Systems Engineer, Health and Life Sciences (Pharma)