Paying for sex once a week: Sex addiction?

Sexual activity is usually considered an addiction when someone's habits are interfering with their lives.  For example: losing a sense of time because you're looking at porn and you're chronically late for work or continuing to have sex in a public place even after prior arrests.  If paying for sex is how you get your sexual needs met and this is not disrupting your life in any way, it does not sounds like addiction.  However, the fact that you are asking appears unusual since in your question, you state that "whatever goes on in private between consenting is OK."  If that's truly the case, then why are you asking.  Perhaps some individual therapy could help you sort out your feelings.  Good luck.