IIRC, it's recommended to refrigerate opened jars of SF jams & fruit for that reason. It's a good idea to refrigerate sugar-sweetened jams & fruit, too, if you're slow at eating them. Husband is all on his own when it comes to eating any kind of fruit, so everything is refrigerated.

Four oz. jelly jars are a good idea - they're especially nice for gifts when you don't know how fast they'll get eaten. It's fun to do a gift basket of 3 different jellies in the 4-oz jars. I have some nice little jelly/jam spoons I put it with the jellies. I don't think there's any way to make them low-carb, but wine jellies are easy & taste great. I miss them.