Why do we get 'bags under our eyes'?
According to the Mayo Clinic website:

As you age, the tissue structures and muscles supporting your eyelids weaken. The skin may start to sag, and fat that is normally confined to the area around the eye (orbit) can move into the area below your eyes. Also, the space below your eyes can accumulate fluid, making the under-eye area appear puffy or swollen. Several factors can lead to this, including:

Fluid retention due to changes in weather (for example, hot, humid days)
hormone levels or eating salty foods
Not getting enough sleep
Allergies or dermatitis, especially if puffiness is accompanied by redness and itching
Heredity — under-eye bags can run in families


Of the list above, the most common reason is likely heredity.
Sources:

Mayo Clinic, as linked above
http://www.allaboutvision.com/cosmetic/puffy-eyes.htm