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The statute says:
"In determining whether an existing award of alimony should be reduced or terminated because of an alleged supportive relationship between an obligee [girlfriend] and a person who is not related by consanguinity or affinity and with whom the obligee resides, [that's you] the court shall elicit the nature and extent of the relationship in question. The court shall give consideration, without limitation, to circumstances, including, but not limited to, the following, in determining the relationship of an obligee to another person"
So, spending lots of nights and weekends together could raise the issue and maybe the person paying alimony would seize on that to ask for a reduction. but I do not think that the Court would reduce the alimony, because hey, she's entitled to have a life. I also do not believe that the overnights would "accumulate" either. If, on the other hand, she's over at your place so much that she doesn't need a home anymore, then you have a problem!
All the best,