Main question
Gravitational redshift for photons are a wellknown phenomena where the electromagnetic radiation is reduced in frequency and thus the wavelenght is increased.
The wave–particle duality is also a wellknown phenomena, even though harder to explain. Particles poses Compton wavelength and the momentum is calculated by taking the derivative of the wavefunction.
A quick analys suggests that it means particles would become "heavier" when near to a massive body (stronger gravitational field). In other words it means that the mass of a particle would increase as it gets closer to e.g. a black hole.
If photons are subjected to gravitational redshift, why aren't all particles subjected to gravitational redshift?
Additional thought
As r approaches infinity, the redshift, expressed as the fractional change of waveleght, varies with the distance R from the center of mass the photon is emitted: $$z(r)=\dfrac{1}{\sqrt{1-\dfrac{2GM}{c^2R}}}-1$$
In the Newtonian limit this becomes: $$z(r)=\dfrac{GM}{c^2R}$$
From e.g. Compton wavelength we can imagine that if the waveleght is changed then the mass also has to change. Using an approximation of circular orbits, the velocity of a star in a galaxy would in the Newtonian limit take the form: $$\dfrac{GMm}{r^2}=ma=\dfrac{mv^2}{r}$$
But if the mass is dependent on the radius, it would look like this: $$\dfrac{GM}{r^2}=\dfrac{kv^2}{r^2}$$ with constant k describing the relation between earth postion in the galaxy and the mass.
In other words, we interestingly enough have more mass in the galaxy then we thougt and a flat rotation curve which is the reason dark matter was invented in the first place.
I want to be clear that I am not suggesting that I in any way solved the dark matter problem. I just wanted to bring up the subject.
