Why is mass uncertain in case of Heisenberg Principle?

As Woody has indicated, there are at least two forms of uncertainty,
Uncertainty inherent in a measurement process such as the minimum length a light microscope will resolve.
Sometimes measurement uncertainty can be circumvented by using a different measurement method eg an electron microscope.
And uncertainty inherent in the mathematical model in use.
Heisenberg uncertainty is of this second type.
Unfortunately, you can't get round this by simply using a different formula for your mathematical model as this would imply that one model contradicts another and they can't both be right.
Heisenberg uncertainty involves momentum and hence mass.
However, again as Woody has indicated, there is yet another quantity involved here. Experimental error.
Experimental error can be eliminated in theory by a perfect experiment.
But finding a perfect experiment would result in the biggest Nobel prize of all time.
The best we have ever been able to do it make lots of repeat experiments and take an average.