Yeah, I know it sucks being alone on Friday and Saturday. And if you don't like to drink too much, it makes it even harder to find things to do! One thing you might want to try, if you're religous, is church (a few have Sat night service). I know it sounds cliche, but there are a lot of quality, caring people there, and if you find the right one (not all of them are of the fire and brimstone variety, try a non-denominational one), you might be pleasantly surprised by the people you find there (as well as the service).
I also know how it feels when you're family hounds you about your lack of a social life, I used to get that all the time until I told my family how that makes me feel. Because mostly they're good people that genuinely care about me, they pretty much don't bug me about it anymore, and realize I have to take this thing at my own pace! You might want to try the same thing with you're family. It's cool that you are grounded enough to realize that they're just doing it because they love you and care about you.
Hope things get better for all of us, and
Peace!
Dazed