It is pretty intuitive that increasing the height or distance of an object and also increasing the mass of it increases the gravitational potential energy (GPE).

Basically the question is asking, with regards to this equation $$U=-\frac{GMm}{r}$$ if you increase mass, this makes the $U$ more negative whilst increasing the distance makes it less negative (closer to 0). This is confusing because even though both increasing distance and mass will increase "GPE", it's not reflected in the output number of the formula, $U$.

Could someone help me understand that although both increase the stored energy, they change in $U$ differently?

No, my question is not a duplicate, as the flagged question asks why $U$ is a negative value, of which I completely understand why it is negative. My question is why the $U$ changes as it does, becoming more negative with more mass which is odd, as it would seem to suggest a decrease in the GPE of the system.