@Sleepingfish , no need to give money if you’re not feeling it. Don’t fret over that. But your kid - that’s different!
At our school, this would be an issue to raise with the Dean. I think it would be worthwhile for them to understand that there are 2 communities here, both of which are expected to enrich the experience of the other, who are struggling to connect. There may be solutions such as a blanket permission for the kids to come to your home or to meet at the local Starbucks. Or maybe the school has some common spaces that can be made available for kids who want to gather.
There are issues that can impede friendships that are structural – the boarders live together 7 days a week and the day students live at home. Policies can permit day students to stay overnight in the dorms from time to time or allow boarders to go home with day students. These may be harder to change.
Administrative issues, like cumbersome sign out processes or rules about where students can gather, are easier to fix.
And there’s the middle group - more activities that involve both groups, both on weekends and when there is no class.
Different schools have worked this out with varying levels of success. The first step is having kids who want to hang out together. Your son could be the catalyst!