Given that skin tags are considered benign, it doesn't surprise me to find very little published research focusing on them. It's unlikely that much grant money exists to answer questions about them.
That said, though, I found a handful of groups that have done some work on them. It seems that they all noticed a statistical relationship between the occurrence of skin tags, obesity and metabolic syndrome. These are the papers describing their research efforts so far:
None of the groups suggest a mechanistic explanation for the occurrence of skin tags, which makes me think that this remains a very open question. However, they all notice a correlation between skin tags and elevated leptin levels.
Leptin is best known as a hunger/satiety regulating hormone. However, it functions through the activation of the JAK/STAT pathway, which in turn activates a number of genes involved in cell survival and in turning off apoptosis, or programmed cell death.
This image comes from this paper in Nature, which, unfortunately, is behind a paywall.
So, my guess based on these data is that increased levels of leptin activate proliferative pathways in cells, leading to the occurrence of skin tags. That this proliferation results in benign cell growth probably has to do with competing tumor-suppressor and related pathways, which I can reasonably assume to be active and functioning, where outright cancer is not present.
What I wonder now, but can't find any information on, is whether skin tags are the only visible evidence of differential cell proliferation, or whether there are other instances within the body. That is, if the leptin-to-skin-tag hypothesis holds, is there something special about skin cells in that response, or are they just the only visible signs of it?