So how is their overall fiscal view? Do they live well below their means, and merely want to splurge a little bit on the weekends? Or are their social plans just one of many leaks in their budget that leaves nothing (or worse, red numbers) at the end of the month?
I used to be at the extreme end of delayed gratification (like you) in some areas, but have loosened up a little with previous gfs, and moreso recently as the stash slowly grows. If this isn't your spouse you're talking about, realize that if their view of money overall (beyond social expenditures) doesn't jive with yours, it will only get WORSE if you are married. You will encounter their spending habits day in and day out, on EVERYTHING. You will notice how they decided to simply splurge on this or that, and they, in turn, will notice you noticing that, and will be offended and annoyed simply because you don't appreciate their cavalier attitude towards spending money.
Also, what bothers me is that you mention that they become visibly annoyed when you mention you don't want to spend the money every weekend on various social activities. Rather than wanting to spend time with you doing anything, or enjoy an activity that you might like, they only seem to want to do what they want, not what possible compromises there may be (something low cost/free this weekend, and then something that cost a few $ more next weekend).
We all have some leakages from a perfect savings plan, so it's natural to budget a little bit of fun money to some activities. IT's up to you to analyze to see if their habits overall would work well with yours.