I hear this question a lot, so here goes.
Heavy tattoos may serve to distinguish the type of girls who get them from other girls who don't, during the same time period and place. But why is that type of girl getting them now, when they didn't back in the '80s, before the craze for piercings and tattoos?
The phenomenon seems even more puzzling because the past 20 years have seen a steady prudification of youth culture. How can we reconcile that with the rising numbers of girls inking up their entire arms?
Prudification goes along with uglification. (See also mid-century art, architecture, and graphic design.) Notice how those girls dress in drab, dark monochrome colors, wear no girly jewelry, and sport flat hair rather than Big Hair. Their sassy, sarcastic, even nasty attitude echos their off-putting look.
Fundamentally, they are part of the larger trend toward drab dressing, and its signal of reluctance to get loose. Their personalities are more anti-social, so they express the neo-Pilgrim style in a more antagonistic fashion than the less abrasive girls in their generation, but they're both variations on the same theme.
Indeed, they look more to the Victorian era or the Fifties pin-up era when taking cues from earlier styles. Not the Romantic-Gothic period of Jane Austen, before the Victorians, nor to the Jazz Age after them. Also not to the New Wave Age after the mid-century and before the current Millennial era. Something about a buttoned-up and settled-down zeitgeist must resonate with them.
They are also part of the larger trend among women toward fear of or hatred toward men. During the date rape hysteria of the early-mid 1990s, mainstream young women (not hardened feminazis) portrayed the typical guy as a predator waiting for the right moment to pounce, or at best a desperate dork who would let his horniness get the better of him in a crucial situation, and force himself on a girl, even though he hadn't planned on it beforehand.
The overt animosity may have calmed down since then, but that's only because the fear, distrust, and aversion toward men has become taken for granted. Try showing signs of a healthy, red-blooded male libido, and you're creepy. In fact, just using the phrase "red-blooded male" marks you as a probable date rapist.
In such a climate, women will alter their appearance and demeanor in order to deflate rather than excite the male libido. They act like prey trying to give warning signals to potential predators. The tattoo chicks are only the extreme version of this widespread trend. Girls sure don't look or act as cute and flirty as they used to in the boy-crazy Eighties, when they thought of guys not as predators but as conspecifics who they wanted to court with engaging mating displays.
Off-putting style also serves to filter out the more assertive and independent males, who would rather spend time on a girl who looks cute, rather than settle for one who's all marked up or not willing to show anything at all. No time to waste in a guessing game, only to suffer from buyer's remorse later. By inking themselves up, girls ensure that only the guys who are willing to get walked over and slapped in the face will approach them. Why go through the long hassle of having your new boyfriend fixed when you can advertise that only the neutered need apply in the first place?
The pervasive effort in falling-crime times to tame violent male nature also seeks to appeal to men's reason -- be more of a family man. But given how little faith they have in men to control their red-blooded nature, they rely on a more extensive program of trying to keep guys from getting too turned on, and to keep them at a distance should that fail. Women understand intuitively that their appearance and demeanor are the main factors that make a guy think she's interested or not, so they adopt drab looks and numb behavior.
The tattooed girls take this to the extreme of off-putting looks and sassy attitude, but qualitatively they're no different from our neo-Victorian / neo-Fifties mainstream.