I really think it's healthy to have a competition system even for a weekend group if you happen to have like 8-10 players. You don't need to play straight for money but for contribution into a pool that will be used to get balls, drinks, hats, food and stuffs for all participants. Basically losers fund the pool. I don't know why I didn't think of this when I still had my weekend group.
An inherent problem with recreational sport is you don't get the same commitment and thus competition. Or at least you are not convinced that other players share the same commitment with you, which makes it hard to make the most of it. Weekend tennis is just too broadly defined. You need a common thread.