Most crystal manufacturers specify the aging of the crystal after one year of operation. A typical range is ±3ppm for the first year. This specification means that the drift of a crystal is unpredictable in direction and magnitude. Although most frequency drift will happen in the first year, some drift will also occur after the first year. Some of the contributing factors in frequency drift is oxidation, and residue inside the encasement attaching to the crystal. This has the effect of changing the total mass of the crystal and thus the resonant frequency. For a more in-depth explanation on this, refer to https://en.wikipedia.org/wiki/Crystal_oscillator#Stability_and_aging.
Load capacitance can change over the years. If it does, it will cause frequency drift, but due to the magnitude of this change and due to the change being symmetric between the crystal pins, this effect is negligible. PCB parasitic capacitance aging, as well as aging of MCU parasitic capacitance, is virtually non-existent. The aging of NP0/C0G type capacitors is less than ±0.1 % for the whole life of the capacitor, i.e. less than 10 fF for a 10 pF capacitor. Considering ppm error, changes in load capacitors give less than 0.1 ppm of drift.
Although PCB parasitic capacitance in general does not age much, adding silicon or urethane on the PCB to add vibration or moisture resistance can slightly alter the capacitance of the PCB tracks as these materials has a different dielectric constant compared to air.