I have been dating a girl for about 6 months. For 2 months she has been sleeping at my place 3 or 4 nights a week. I sleep at her place maybe once a week. I don't spend much money on her. Dinner or lunch maybe 2 or 3 times a week though nothing too fancy. She pays once in awhile.
My concern is if we break up while casually dating would she be able to sue me for support?
My home is much nicer than hers and my net worth is substantial while she doesn't have much monetary assets.
Please advise.
Thanks

In short, NO.

In the US, no there is no support unless you are married.

And she can not sue you for the value of the sex but of course you should be treating her better unless she is just a sex buddy

I don't think you can "sue someone for support" if you're only dating (not in Europe either.)

Perhaps you should be more concerned about the reason why you ask the question in the first place?