What causes these stretch marks?
Stretch marks (striae) are caused by intradermal tears, that means tears that occur within the skin layers. These tears are caused when two things happen at the same time.
The skin is stretching at a high rate. This happens when you gain weight rapidly, are pregnant, or are otherwise undergoing changes in body shape - as happens during the adolescent and teenage years.
There's not enough new collagen being synthesized in the skin to accommodate that stretching.
Is it common to get them at a young age?
Yes - in this case meaning adolescent and teenage years. The reasons are twofold:
First, these are years when your body is undergoing changes in shape and composition. The skin has to stretch to accommodate these changes.
Second, something we haven't discussed yet is the effect of cortisol on collagen synthesis. Cortisone is a steroid hormone produced by the adrenal gland in response to stress among other things. It's been shown to inhibit collagen synthesis, effectively making the skin (and cartilage in the joints) less stretchy.
Are they more common in some people than others (besides what was mentioned above?)
People with increased adrenal cortical activity, such as teenagers and those with Cushing's disease.
"The cause of striae distensae"
"Effects of cortisol acetate on collagen biosynthesis..."