They have a name for it. And it's

[77ncaachamps]

Tanorexia

Who knew? 

"Tanorexia: addiction to Tannings

Tanorexia is an unhealthy dependence on tanning; the name comes because of its similarities to both substance addictions and body image disorders, such as anorexia. There is some evidence that UV tanning dependence may have biological underpinnings like other addictions, such as the production of endorphins as in the 'runner's high, but since tanning dependence is such a new concept, treatments are still being studied."

http://oddee.com/item_96496.aspx (Odee's a great site!)

[BrewCity83]

Tanorexia Nervosa; The manic combination of excessive artificial tanning and constant pacing, fueled by overconsumption of Diet Pepsi.  Side effects can include an inflated opinion of onesself.