It is normal family banter. Like I said, I wasn't there (and you weren't there) so we're not aware of the circumstances. But in my family, it would be completely alright for my uncle to walk into a room and get on his knee before my unmarried twenty year old cousin (not his daughter, his sisters daughter) and say, "Will you marry me, _____" Then we all burst into laughter and have a meal together.

It would also not be odd for one of my female cousins to tell my other female cousins, in a completely serious voice, "I want to be with you so bad." And then awkwardly hug her too tight. It's a form of humor that sometimes happens in families. The goal is either to make an obviously fake or messed up situation to help break the ice for the evening or just make everyone laugh. Sometimes, that includes saying some awkward shit that, in another context, would be extremely creepy.

A lot of families are close enough and know each other well enough where that humor is pretty normal and isn't crossing the line.

And again, I wasn't there and I don't know the family. But from the description given by /u/mariahmeows I wouldn't be surprised if the cousin was just trying to make her feel weird because he found it funny. That, or he just thought it was something amusing to say to a six-year-old cousin. Or maybe the guy was just a pedophile and wanted to marry his six-year-old cousin. But, if all he said is he wants to marry her, I don't really think that is the case. If, however, other issues came up over the years (such as inappropriate touching), then it would be a completely different case. I'm just going off the information provided.